Difference between revisions of "009B Sample Midterm 1, Problem 1"

Revision as of 18:42, 19 January 2016

Evaluate the indefinite and definite integrals.

a)

\int x^{2}{\sqrt {1+x^{3}}}dx

b)

\int _{\frac {\pi }{4}}^{\frac {\pi }{2}}{\frac {\cos(x)}{\sin ^{2}(x)}}dx

Solution:

ExpandFinal Answer:

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-<span class="exam">Divide the interval <math>[0,\pi]</math> into four subintervals of equal length <math>\frac{\pi}{4}</math> and compute the right-endpoint Riemann sum of <math>y=\sin (x)</math>
+<span class="exam">Evaluate the indefinite and definite integrals.
+::<span class="exam">a) <math>\int x^2\sqrt{1+x^3}dx</math>
+::<span class="exam">b) <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}dx</math>