See the abundant list of Calculus step-by-step solutions available
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(Solved) Find the volume of the solid obtained by rotating the region bounded by the given curves about the s #18927
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(Solved) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region #18928
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[Solution] A spring has a natural length of 20 cm. If a 25?N force is required to keep it stretched to a length #18929
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[Solution] A chain lying on the ground is 10 m long and its mass is 80 kg. How much work is required to raise o #18930
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[Solved] f(x)=√{x}, [0,4] (a) Find the average value off on the given interval (b) Find c such that fav #18931
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(Solved) Sketch the region bounded by the graphs of the algebraic functions and find the area of the region. #18932
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[Solution] Find the volume of the solid obtained by rotating the region bounded by the given curves about the s #18933
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(Solved) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region #18934
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Solution: f(x)=√{x}, [0,4] (a) Find the average value off on the given interval (b) Find c such that fav #18937
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[Solution] Let g(x)=∫_{-2}^x{f(t)dt} where f is the function whose graph is shown. (a) Evaluate g(0) g(3). #18938
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(Solved) Evaluate the integral ∫_0^1{(4+x^2√{x})dx} #18940
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[Solved] Evaluate the integral ∫_{0}^{π /4}{ sec θ tan θ dθ } #18941
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[Solution] Evaluate the indefinite integral ∫{((1)/(y^2)+3-2y)dy} #18942
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[Solution] Evaluate the integral ∫{(2v+3)(3v-4)dv} #18943
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Solution: Evaluate the integral ∫_{π /6}^{π /3}{(1)/({{ sin )^2}x}dx} #18944
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[Solved] Evaluate the indefinite integral ∫{(3x)/(√{x^2+1)}dx} #18945
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[Solution] Evaluate ∫{ cos x{{ sec }^2}x tan x sec xdx} #18946
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(See Solution) Evaluate the following definite integral: ∫_0^2{x√{4-x^2}dx} #18947
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[Solved] Estimate the area under the graph of f(x)=3√{x} from x = 1 to x = 9 using 8 approximating rect #18948
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[Solved] Express the area under the curve f(x)=x^4+3x^3-x as a limit from 3 to 8. Use an algebraic computer s #18949
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(Solved) Speedometers for a speedboat at 10 second intervals are given in the table. t(s) 0 10 20 30 40 50 v( #18950
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(See Solution) Use the Midpoint Rule with the given value of n to approximate the integral. Round to 4 decimal plac #18951
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(Solved) Express the limit as a definite integral on the given interval. {n→ ∞ } lim ∑lim #18953
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[Solved] Evaluate the integral by interpreting it in terms of areas. ∫_{-4}^2{|x+4|dx} #18955
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[Solved] Use the properties of integrals and the definition to compute ∫_1^4{(x^2-4x+5)dx} #18956
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[Solved] Bids for a government contract are supposed to be opened in a random order. For a given contract, th #19101
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[Solution] Demand and Revenue: The manager of a company that produces graphing calculators determines that when #19105
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[Solution] Among all pairs of numbers whose sum is 200, find a pair whose product is as large as possible. What #19503
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(Solved) The Equation A = 53.7e0.001t models the population of a country, A, in millions, t years after 2005. #19511
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[Solved] Find the indefinite integral ∫{6dx} #19575
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(Solved) Find the indefinite integral ∫{{{x}^{-4}}dx} #19576
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[Solution] Find the indefinite integral ∫{{{x}^{2/3}}dx} #19577
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[Solved] Find the indefinite integral ∫{(2)/(x^2)dx} #19578
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Solution: Find the indefinite integral ∫{(3-2x)dx} #19579
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[Solved] Find the indefinite integral ∫{(4x^3-(2)/(x^2)-1)dx} #19580
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[Solved] Find the indefinite integral ∫{(√{x}+(3)/(√{x)})dx} #19581
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(See Solution) Find the indefinite integral ∫{(2t+1)(t-2)dx} #19582
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Solution: If f'(x)=2x+1 and f(1)=3, compute f(x) #19583
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[Solution] Find the indefinite integral: ∫{4{{(4x+3)}^4}dx} #19584
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[Solved] Find the indefinite integral: ∫{{{(x^3-2x)}^2}(3x^2-2)dx} #19585
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(See Solution) Find the indefinite integral: ∫{(4x)/({{(2x^2+3))^3}}dx} #19586
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(Solved) Find the indefinite integral: ∫{3{t^2}√{{t^3}+2}dt} #19587
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Solution: Find the indefinite integral: ∫{{{(x^2-1)}^9}xdx} #19588
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Solution: Differentiate f(x)=5x^3-(2)/(3x^3) #19594
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[Solution] Differentiate f(x)=√{x}-(2)/(√{x)} #19595
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[Solution] Differentiate f(x)=(x+2)/(x-1) #19596
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[Solution] Differentiate f(x)={{(4x^2+3x-1)}^{3/2}} #19597
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[Solution] Differentiate f(x)=(x^2+1)(2x^2-(1)/(x)) #19598
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[Solved] Differentiate f(t)={{({{t}^{-2}}-{{t}^{-3}})}^4} #19599
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[Solved] Differentiate f(x)={{((x-1)/(x+2))}^4} #19600
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[Solution] Find the derivative of the given function and evaluate f'(x) at the given value of x: f(x)=(x^ #19601
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Solution: Integrate ∫{(8x^3+6x-2)dx} #19602
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(See Solution) Integrate ∫{(2{{x}^{1/2}}-{{x}^{2/5}})dx} #19603
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Solution: Integrate ∫{((4)/(x^3)+(x^3)/(4))dx} #19604
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(Solved) Integrate ∫{(5y-3)(3y-2)dy} #19605
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(Solved) Integrate ∫{x^2{{(x^3+2)}^{10}}dx} #19606
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Solution: Find the function f(x) such that f'(x)=6x^2-4x+7 and f(1)=3. #19607
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Solution: Evaluate the definite integral ∫_0^2{(4x^3-9x^2+2x-1)} #19608
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Solution: Find the area of the region bounded by the graphs of the functions f(x)=x^2+9 and g(x)=x, and the v #19609
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(See Solution) Simplify (3x^2+4x+1)-(x^2 +x-2). #19623
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[Solution] Show that every member of the family of functions y=((ln x+C))/(x) is a solution of the differential #19687
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Solution: A function y(t) satisfies the differential equation (dy)/(dt)=y^4-6y^3+5y^2 (a) What are #19688
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[Solved] Find the area of the region bounded by the graph of yquad = (x)/({{x)^{ 2}}quad + 1}, the x -axis, a #19689
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(Solved) Find the derivative: yquad = {e^{ x}} ( sin xquad + cos x) #19690
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(See Solution) Find ∫{(dx)/({{({{x)^{ 2}}quad + 1)}^{{}^3!_{2};}}}} #19691
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[Solved] Find ∫{{{x}^{ 2}} ln xdx} #19692
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[Solution] Find the volume of the solid generated by revolving the region bounded by the graphs of the equation #19693
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Solution: Find the arc length of the graph of the function yquad = ({{x}^{ 5}})/(10)quad + (1)/(6 {{x)^{ 3}}} #19694
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[Solved] A barn is 100 feet long and 40 feet wide. A cross section of the barn’s roof is the inverted caterna #19695
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[Solved] Solve the differential equation {y}' - 2 x yquad = 0 #19696
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[Solution] Find the derivative of the function yquad = ln √{{{x}^{ 2}}quad - 4}. #19699
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[Solution] Find the indefinite integral and check the result by differentiation: ∫{{{u}^{ 2}} √{{{u}^ #19700
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[Solved] A quantity of gas with an initial volume of 1 cubic foot and a pressure of 500 pounds per square foo #19701
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[Solution] Find the derivative of the function yquad = {e^{ √{x}}} #19702
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[Solution] Find the definite integral: ∫_0^1{{e^{ - 2 x}}dx} #19703
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[Solved] Find the indefinite integral: ∫{x {e^{ x}}dx} #19704
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[Solved] Find ∫{(dx)/({{x)^{ 2}} √{9quad - {{x}^{ 2}}}}} #19705
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[Solution] Find ∫_{√{3}}^2{(√{{{x}^{ 2}}quad - 3})/(x)}dx #19706
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Solution: Find the ∂ fraction expansion: (4 {{x}^{ 2}}quad + 3)/({{(xquad - 5))^{ 3}}} #19707
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Solution: A circular oil spill has been created by a ship. As the ship leaks oil, the radius of the spill is g #19962
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(See Solution) Explain which equation is a better candidate for logarithmic differentiation. Use the best approach #20055
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[Solved] A particle moves from right to left along the curve y=√{x} in such a way that the x-coordinate #20056
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[Solved] About how accurately must the interior of a 10 meter high cylindrical storage tank be measured to ca #20057
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[Solved] Find the equation of the tangent to the curve e X+ y2 = 2 at the point (0 , 1). #20058
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[Solved] Let f(x)=({e^x}-{e^{-x}})/(2) and sketch the graph of f(x) using the curve sketching techniques cove #20059
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(Solved) Find ∫{(4+√{t})/({t^3)}dt} and verify your result by differentiation. #20060
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[Solved] Find the exact area under the curve f(x) = { e X , x ? 3 { - (x - 3)2 + 16 , x > 3 from x=1 to #20062
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Solution: Find all extreme values of f(x) = (4/ x) + ln (x^2) on the interval [1,4]. #20063
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[Solution] Show that (d)/(dx)((x)/(x+1))=(d)/(dx)(-(1)/(x+1)) even though (x)/(x+1)≠ (-1)/(x+ #20064
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[Solution] Find the absolute extrema of the function f(x) = e X+ e -X / 2 on the interval [ -2, 1]. #20065
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Solution: Use the Curve Sketching procedure to sketch the graph of y = x1/3 (x^2 - 4), be sure to label all #20066
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[Solved] Take the limit. (A) {x→ ∞ } lim ({{7}^x}-1)/(x)((∞ ;{∞ }))/({=)} (B) {x&r #20067
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(Solved) Use the Curve Sketching procedure to sketch the graph of y = In(x2 - 4x + 3) be sure to label all #20068
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(Solved) Use the Curve Sketching procedure to sketch the graph of y = (x+1) / (x^2- 4) , be sure to label a #20069
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[Solved] The sum of two nonnegative numbers is 30. Find the numbers if the product of twice the first numbe #20070
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[Solution] True or False, explain your result. The function f() = x3 + x + 1 has an absolute maximum on (-? #20071
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[Solution] Find the number in [2, 5] where the average rate of change is equal to the instantaneous rate of c #20072
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[Solved] Write the equation using {{2}^a}=d logarithms #20075
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[Solved] Find all values of x at which g(x)=(x-2)/(x-5) is not continuous. #20078
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[Solution] Find the average rate of change of y=√{2x+1} between x = 4 and x = 12. #20079
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[Solved] Find the derivative of y=7x^2{e^{3x}}. #20080
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Solution: Find the derivative of y=(ln (3x))/(x+1) #20081
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