Use substitution to evaluate the following integrals.
Use integration by parts to evaluate the following integrals.
- R cos(x)ln(sinx)dx
Problem 2
- Prove the reduction formula
Hint: Use integration by parts and the fact that cos2(x) + sin2(x) = 1.
- Suppose that f : R→R continuous and odd, i.e., satisfies −f(x) = f(−x). Show that
.
Problem 3
Using 2a)
Z
- Evaluate cos2(x)dx.
Z
- Evaluate cos3(x)dx.
- Evaluate.
Bonus:
We will cover this on Tuesday, 26.11:
Find the area between the curves x = 1 − y2 and y = −2x − 1.
Hint: At the end, integrate with respect to y not x.
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