Integration by Parts

$\begingroup$

Question 1

a)

Evaluate $\int_0^\pi x \cos(x) \mathrm{dx}$ using integration by parts, letting $u = x$ and $\mathrm{dv} = \cos(x)$

Expected answer:

Score: 0/1

Show feedback

This feedback is based on your last submitted answer. Save your changed answer to get updated feedback.

Or, you could:

There's nothing more to do from here.

b)

Evaluate $\int_1^\var{b}x^\var{a}\ln(x)\mathrm{dx}$ using integration by parts, letting $u = \ln(x)$ and $\mathrm{dv} = x^\var{a}$ .

Answer: interpreted as $\displaystyle{}$ Expected answer:interpreted as $\displaystyle{\frac{ 64 }{ 3 }}$ ln(4)+interpreted as $\displaystyle{}$ Expected answer:interpreted as $\displaystyle{-\frac{ 64 }{ 9 } + \frac{ 1 }{ 9 }}$

Score: 0/2

Show feedback

This feedback is based on your last submitted answer. Save your changed answer to get updated feedback.

Or, you could:

There's nothing more to do from here.

c)

Evaluate $\int_0^{1/2}x\cos(x)\mathrm{dx}$ using the substitution $u = x$ and $\mathrm{dv} = \cos(\pi x)\mathrm{dx}$ .

When writing $\pi$ in your answer simly write pi.

$\displaystyle{}$ Expected answer:

$\displaystyle{\frac{ 1 }{ 2 \pi } - \frac{ 1 }{ \pi^{2} }}$

Score: 0/1

Show feedback

This feedback is based on your last submitted answer. Save your changed answer to get updated feedback.

Or, you could:

There's nothing more to do from here.

Advice

Use Integration by Parts

$\endgroup$

Numbas has failed

Integration by Parts

a)

b)

c)

Advice