Difference between revisions of "009B Sample Midterm 2, Problem 2"

Revision as of 18:47, 19 January 2016

This problem has three parts:

a) State the fundamental theorem of calculus.

b) Compute

{\frac {d}{dx}}\int _{0}^{\cos(x)}\sin(t)dt

c) Evaluate

\int _{0}^{\frac {\pi }{4}}\sec ^{2}xdx

Solution:

Final Answer:

@@ Line 1: / Line 1: @@
-<span class="exam">Evaluate the indefinite and definite integrals.
+<span class="exam">This problem has three parts:
-::<span class="exam">a) <math>\int x^2\sqrt{1+x^3}dx</math>
+::<span class="exam">a) State the fundamental theorem of calculus.
-::<span class="exam">b) <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}dx</math>
+::<span class="exam">b) Compute <math>\frac{d}{dx}\int_0^{\cos (x)}\sin (t)dt</math>
+::<span class="exam">c) Evaluate <math>\int_{0}^{\frac{\pi}{4}}\sec^2 xdx</math>