Calculus/Integration/Solutions

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Integration of Polynomials[edit]

Evaluate the following:

1.

2.

3.

4.

5.

Indefinite Integration[edit]

Find the general antiderivative of the following:

6.

7.

8.

9.

10.

11.

12.

13.

Let

Then

Integration by parts[edit]

14. Consider the integral . Find the integral in two different ways. (a) Integrate by parts with and . (b) Integrate by parts with and . Compare your answers. Are they the same?

(a)


(b)

Notice that the answers in parts (a) and (b) are not equal. However, since indefinite integrals include a constant term, we expect that the answers we found will differ by a constant. Indeed