Difference between revisions of "009B Sample Final 3, Problem 2"

Revision as of 13:29, 28 February 2017

Evaluate the following integrals.

(a) $\int _{0}^{\frac {\sqrt {3}}{4}}{\frac {1}{1+16x^{2}}}~dx$

(b) $\int {\frac {x^{2}}{(1+x^{3})^{2}}}$

(c) $\int _{1}^{e}{\frac {\cos(\ln(x))}{x}}~dx$

Solution:

(a)

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

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 <span class="exam"> Evaluate the following integrals.
-<span class="exam">(a) <math>\int_0^{\frac{\sqrt{3}}{4}} \frac{1}{1+16x^2}~dx</math>
+<span class="exam">(a) &nbsp;<math>\int_0^{\frac{\sqrt{3}}{4}} \frac{1}{1+16x^2}~dx</math>
-<span class="exam">(b) <math>\int \frac{x^2}{(1+x^3)^2}</math>
+<span class="exam">(b) &nbsp;<math>\int \frac{x^2}{(1+x^3)^2}</math>
-<span class="exam">(c) <math>\int_1^e \frac{\cos(\ln(x))}{x}~dx</math>
+<span class="exam">(c) &nbsp;<math>\int_1^e \frac{\cos(\ln(x))}{x}~dx</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"