Difference between revisions of "009B Sample Final 3, Problem 7"

Revision as of 11:04, 18 February 2017

Does the following integral converge or diverge? Prove your answer!

\int _{1}^{\infty }{\frac {\sin ^{2}(x)}{x^{3}}}~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">Does the following integral converge or diverge? Prove your answer!
-::::::::<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.
+::::<math>\int_1^\infty \frac{\sin^2(x)}{x^3}~dx</math>
-<span class="exam">b) Using the upper sum with three rectangles having equal width, approximate the area.
-<span class="exam">c) Find the actual area of the region.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"