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A list of problems from a university-level math 252 calculus quiz. Students are required to find antiderivatives or evaluate definite integrals using various integration techniques such as integration by parts, substitution, and trigonometric substitution. The document also includes hints to help guide the students in solving the problems.
Typology: Quizzes
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Find the antiderivative or value of the definite integral as appropriate. You must show your work to get credit. p.457, #8^ ∫ x^2 cos( mx ) dx. Hint: Integration by parts. p.457, #28^ ∫^12 (ln x^ x 3 )^2 dx. Hint: First make the substitution u = ln x , then try integration by parts. p.465, #16^ ∫ cos θ cos^5 (sin θ ) dθ. p.468, #38^ ∫^ π/π/ 42 cot^3 x dx.
p.472, #6^ ∫^12 √ x (^2) − 1 x dx. Hint: Try a trig. substitution.
March 11, 2009
