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Expert-verified Found in: Page 416 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample. (a) True/False: $\int {g}^{\mathrm{\prime }}\left(h\left(x\right)\right){h}^{\mathrm{\prime }}\left(x\right)dx=g\left(h\left(x\right)\right)+C$(b) True/False: If $v={u}^{2}+1,$ then $\int \sqrt{{u}^{2}+1}du=\int \sqrt{v}dv$(c) True/False: If $u={x}^{3},$ then $\int x\mathrm{sin}\left({x}^{3}\right)dx=\frac{1}{3x}\int \mathrm{sin}udu$(d) True/False: ${\int }_{0}^{3} {u}^{2}du={\int }_{x=0}^{x=3} \left(u\left(x\right){\right)}^{2}du$(e) True/False: ${\int }_{0}^{1} {x}^{2}dx={\int }_{0}^{1} {u}^{2}du$(f) True/False: localid="1654067255916" ${\int }_{2}^{4} x{e}^{{x}^{2}-1}dx=\frac{1}{2}{\int }_{2}^{4} {e}^{u}du$ (g) True/False: ${\int }_{2}^{3} f\left(u\left(x\right)\right){u}^{\mathrm{\prime }}\left(x\right)dx={\int }_{u\left(2\right)}^{u\left(3\right)} f\left(u\right)du$(h) True/False: ${\int }_{0}^{6} f\left(u\left(x\right)\right){u}^{\mathrm{\prime }}\left(x\right)dx={\left[\int f\left(u\right)du\right]}_{0}^{6}$

(part a)

(part b)

(part c)

(part d)

(part e)

(part f)

(part g)

(part h)

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## Step17: Explanation (part h).

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