136.169, Assignment No.5

March 12, 2003

The assignment is due Wednesday, March 19 in class. Late assignments receive a mark zero.

1. Evaluate the following integrals:

a) [5]

b) [5]

c) [5]

2. If exists and is continuous on [a,b] and f(a) = f(b) = 0, show that

. [6]

( Hint : use integration by parts twice on the right hand side.)

3. Obtain a reduction formula for (where n3) and use it to find

. [7]

4. Find the area inside both of the circles and . [7]

5. Show that the integral I = converges and that it value satisfies I < .

[6]

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Total [41/40]