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

Revision as of 09:42, 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:

@@ Line 1: / Line 1: @@
-<span class="exam">Consider the region bounded by the following two functions:
+<span class="exam">Evaluate the following integrals or show that they are divergent:
-::::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math style="vertical-align: -4px">y=0</math>.
-<span class="exam">a) Using the lower sum with three rectangles having equal width, approximate the area.
+::<span class="exam">a) <math>\int_1^\infty \frac{\ln x}{x^4}~dx</math>
-<span class="exam">b) Using the upper sum with three rectangles having equal width, approximate the area.
+::<span class="exam">b) <math> \int_0^1 \frac{3\ln x}{\sqrt{x}}~dx</math>
-<span class="exam">c) Find the actual area of the region.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"