MATH 152, FALL 2009CALCULUS II FOR THE MATHEMATICAL AND PHYSICAL SCIENCESHINTS ON MIDTERM EXAM I ON OCTOBER 5, 2009Question 1.You need to integrated the two integrals separately, one using the technique for odd powersof sine and cosine, the other one using the technique for cos2(double angle formula from the Calc I sheet!).The first integral gives you2/99.Question 2.Version A:The integral to write down isRπ02π(4-x)xsinx dx. You need to explain thiscarefully from the sketch of the shell (i.e. determine the radius). Then you need to apply integration byparts to get8π2+8π-2π3.Version B:The integral to write down isRπ/202π(2-x)xcosx dx. Youneed to explain this carefully from the sketch of the shell (i.e. determine the radius). Then you need toapply integration by parts to getπ2/2(4-π).Question 3.This question was meant to be done using integration by fractional parts, but it can alsobe done using u-substitution. The correct factorization of the denominator is(2t+1)2
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