Problem Set 7
1
CHALLENGE PROBLEMS CARIBBEAN SCIENCE FOUNDATION SPISE 2013 Calculus II Problem Set 7 1. Given I n = Z x n √ a 2 + x 2 dx, n ≥ 2 derive a reduction formula for I n . Hence, evaluate 2 Z 0 x 5 √ 5+ x 2 dx. 2. Evaluate π R 0 x 1 + sin x dx. 3. Prove that if n is a positive integer, 1 Z 0 x n √ 1 - x dx = 2 2n+2 n!(n + 1)! (2n + 3)! .
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Transcript of Problem Set 7
CHALLENGE PROBLEMS
CARIBBEAN SCIENCE FOUNDATIONSPISE 2013 Calculus II
Problem Set 7
1. Given
In =
∫xn√
a2 + x2dx, n ≥ 2
derive a reduction formula for In. Hence, evaluate
2∫0
x5
√5 + x2
dx.
2. Evaluateπ∫0
x
1 + sin xdx.
3. Prove that if n is a positive integer,
1∫0
xn√1− x dx =
22n+2 n!(n+ 1)!
(2n+ 3)!.
