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Two problems related to improper integrals from a calculus ii quiz held in fall 2005. The first problem asks to determine the convergence or divergence of the integral ∫from 0 to π/2 of sin(x)cos(x) dx using antiderivative. The second problem asks to use comparison test to determine the convergence or divergence of the integral ∫from 0 to ∞ of 1/√(x^2 + 1) dx.
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QUIZ 7
Show ALL your work CAREFULLY.
(a) Determine whether the following improper integral converges or di- verges by using antiderivative. ∫ (^) π/ 2
0
sin x cos x
dx
(b) Use comparison to determine whether the following improper integral converges or diverges. (^) ∫ ∞
1
dx √ x^4 + x^2 + 1
Date: November 2, 2005. 1
