Difference between revisions of "009B Sample Final 3, Problem 5"

Revision as of 10:59, 18 February 2017

Find the following integrals.

a)

\int x\cos(x)~dx

b)

\int \sin ^{3}(x)\cos ^{2}(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"> Find the following integrals.
-::::::::<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 x\cos(x)~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 \sin^3(x)\cos^2(x)~dx</math>
-<span class="exam">c) Find the actual area of the region.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"