(See Steps) Let B(x)=-1/2x^2 for x < 0 and B(x)=1/2x^2 for x > 0. Show that ∫_a^b|x|dx=B(b)-B(a)
Question: Let \(B\left( x \right)=-\frac{1}{2}{{x}^{2}}\) for x < 0 and \(B\left( x \right)=\frac{1}{2}{{x}^{2}}\) for x > 0. Show that \(\int\limits_{a}^{b}{|x|dx}=B\left( b \right)-B\left( a \right)\) .
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![[All Steps] Let f : [a, b]](/images/solutions/MC-solution-library-31046.jpg "[All Steps] Let f : [a, b] → R be continuous on [a, b] and let")
[All Steps] Let f : [a, b] → R be continuous on [a, b] and let
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[Steps Shown] If f : R → R is continuous and c > 0, define
(See Solution) Compute the following integrals ∫_0^1t√1+t^2dt
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[Steps Shown] Use Mathematical Induction and Theorem 7.1.4 to
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[See Steps] If f ∈ R and |f(x)| ≤ M for all x € [a, b],
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