Difference between revisions of "009B Sample Final 2, Problem 7"

Revision as of 19:20, 18 February 2017

Evaluate the following integrals or show that they are divergent:

(a) $\int _{1}^{\infty }{\frac {\ln x}{x^{4}}}~dx$

(b) $\int _{0}^{1}{\frac {3\ln x}{\sqrt {x}}}~dx$

Solution:

(a)

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

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 <span class="exam">Evaluate the following integrals or show that they are divergent:
-::<span class="exam">a) <math>\int_1^\infty \frac{\ln x}{x^4}~dx</math>
+<span class="exam">(a) <math>\int_1^\infty \frac{\ln x}{x^4}~dx</math>
-::<span class="exam">b) <math> \int_0^1 \frac{3\ln x}{\sqrt{x}}~dx</math>
+<span class="exam">(b) <math> \int_0^1 \frac{3\ln x}{\sqrt{x}}~dx</math>
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 |}
 '''Solution:'''
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 |}
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