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152MidtermIAsols

# 152MidtermIAsols - MATH 152 FALL 2009 CALCULUS II FOR THE...

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MATH 152, FALL 2009 CALCULUS II FOR THE MATHEMATICAL AND PHYSICAL SCIENCES HINTS ON MIDTERM EXAM I ON OCTOBER 5, 2009 Question 1. You need to integrated the two integrals separately, one using the technique for odd powers of sine and cosine, the other one using the technique for cos 2 (double angle formula from the Calc I sheet!). The first integral gives you 2/99 . Question 2. Version A: The integral to write down is R π 0 2 π ( 4 - x ) x sin x dx. You need to explain this carefully from the sketch of the shell (i.e. determine the radius). Then you need to apply integration by parts to get 8 π 2 + 8 π - 2 π 3 . Version B: The integral to write down is R π /2 0 2 π ( 2 - x ) x cos x dx. You need to explain this carefully from the sketch of the shell (i.e. determine the radius). Then you need to apply integration by parts to get π 2 /2 ( 4 - π ) . Question 3. This question was meant to be done using integration by fractional parts, but it can also be done using u-substitution. The correct factorization of the denominator is ( 2 t + 1 ) 2
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