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Expert-verifiedFound in: Page 416

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: $\int {g}^{\mathrm{\prime}}\left(h\right(x\left)\right){h}^{\mathrm{\prime}}\left(x\right)dx=g\left(h\right(x\left)\right)+C$

(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: ${\int}_{0}^{3}\u200a{u}^{2}du={\int}_{x=0}^{x=3}\u200a\left(u\right(x){)}^{2}du$

(e) True/False: ${\int}_{0}^{1}\u200a{x}^{2}dx={\int}_{0}^{1}\u200a{u}^{2}du$

(f) True/False: localid="1654067255916" ${\int}_{2}^{4}\u200ax{e}^{{x}^{2}-1}dx=\frac{1}{2}{\int}_{2}^{4}\u200a{e}^{u}du$

(g) True/False: ${\int}_{2}^{3}\u200af\left(u\right(x\left)\right){u}^{\mathrm{\prime}}\left(x\right)dx={\int}_{u\left(2\right)}^{u\left(3\right)}\u200af\left(u\right)du$

(h) True/False:

${\int}_{0}^{6}\u200af\left(u\right(x\left)\right){u}^{\mathrm{\prime}}\left(x\right)dx={\left[\int f\left(u\right)du\right]}_{0}^{6}$(part a)

(part b)

(part c)

(part d)

(part e)

(part f)

(part g)

(part h)

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