Difference between revisions of "009B Sample Final 1, Problem 4"

Revision as of 19:57, 1 February 2016

Compute the following integrals.

a)

\int e^{x}(x+\sin(e^{x}))~dx

b)

\int {\frac {2x^{2}+1}{2x^{2}+x}}~dx

c)

\int \sin ^{3}x~dx

Foundations:

Solution:

(a)

(b)

Step 2:

Step 3:

(c)

Step 1:

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