[Solution] Let f : [a, b] → R be continuous on [a, b] and let v : [c ,d] → R be differentiable on [c, d] with v([ c,d ])⊆ [ a,b ] . If we
Question: Let f : [a, b] \(\to \mathbb{R}\) be continuous on [a, b] and let \(v\) : [c ,d] \(\to \mathbb{R}\) be differentiable on [c, d] with \(v\left( \left[ c,d \right] \right)\subseteq \left[ a,b \right]\) . If we define \(G\left( x \right)=\int\limits_{a}^{v\left( x \right)}{f}\) show that G'(x) = f(v(x)) v'(x) for all x \(\in \) [c, d].
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![[Steps Shown] If f : R →](/images/solutions/MC-solution-library-31047.jpg "[Steps Shown] If f : R → R is continuous and c > 0, define")
[Steps Shown] If f : R → R is continuous and c > 0, define
(See Solution) Compute the following integrals ∫_0^1t√1+t^2dt
![[Steps Shown] Use Mathematical Induction and Theorem](/images/solutions/MC-solution-library-31049.jpg "[Steps Shown] Use Mathematical Induction and Theorem 7.1.4 to")
[Steps Shown] Use Mathematical Induction and Theorem 7.1.4 to
![[See Steps] If f ∈ R and](/images/solutions/MC-solution-library-31050.jpg "[See Steps] If f ∈ R and |f(x)| ≤ M for all x € [a, b],")
[See Steps] If f ∈ R and |f(x)| ≤ M for all x € [a, b],
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[Steps Shown] Let g(x) = 0 if x ∈ [0, 1] is rational and
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