Difference between revisions of "009B Sample Final 2, Problem 6"

Revision as of 13:50, 3 March 2017

Evaluate the following integrals:

(a) $\int {\frac {dx}{x^{2}{\sqrt {x^{2}-16}}}}$

(b) $\int _{-\pi }^{\pi }\sin ^{3}x\cos ^{3}x~dx$

(c) $\int _{0}^{1}{\frac {x-3}{x^{2}+6x+5}}~dx$

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 \frac{dx}{x^2\sqrt{x^2-16}}</math>
+<span class="exam">(a) &nbsp;<math>\int \frac{dx}{x^2\sqrt{x^2-16}}</math>
-<span class="exam">(b) <math>\int_{-\pi}^\pi \sin^3x\cos^3x~dx</math>
+<span class="exam">(b) &nbsp;<math>\int_{-\pi}^\pi \sin^3x\cos^3x~dx</math>
-<span class="exam">(c) <math>\int_0^1 \frac{x-3}{x^2+6x+5}~dx</math>
+<span class="exam">(c) &nbsp;<math>\int_0^1 \frac{x-3}{x^2+6x+5}~dx</math>
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