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[9] 1. Evaluate the integral .

Set and . We find that and that . Using integration by parts we get .

[8] 2.

[4] (a) Simplify , where (show your work).

[4] (b) Differentiate . Do not simplify your answer.

(a) Set , so that we want . means . Since is between 0 and and we can represent it by an angle in a right angled triangle.

In the picture and .

(b)

[8] 3. Evaluate .

Set ; so . Then we have