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

Revision as of 15:42, 4 March 2017

Find the area of the region between the two curves $y=3x-x^{2}$ and $y=2x^{3}-x^{2}-5x.$

Foundations:
1. You can find the intersection points of two functions, say $f(x),g(x),$
by setting $f(x)=g(x)$ and solving for $x.$
2. The area between two functions, $f(x)$ and $g(x),$ is given by $\int _{a}^{b}f(x)-g(x)~dx$
for $a\leq x\leq b,$ where $f(x)$ is the upper function and $g(x)$ is the lower function.

Solution:

Final Answer:

@@ Line 4: / Line 4: @@
 !Foundations: &nbsp;
 |-
-|
+|'''1.''' You can find the intersection points of two functions, say &nbsp;<math style="vertical-align: -5px">f(x),g(x),</math>
 |-
 |
+&nbsp; &nbsp; &nbsp; &nbsp;by setting &nbsp;<math style="vertical-align: -5px">f(x)=g(x)</math>&nbsp; and solving for &nbsp;<math style="vertical-align: 0px">x.</math>
 |-
-|
+|'''2.''' The area between two functions, &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">g(x),</math>&nbsp; is given by &nbsp;<math>\int_a^b f(x)-g(x)~dx</math>
 |-
 |
+&nbsp; &nbsp; &nbsp; &nbsp;for &nbsp;<math style="vertical-align: -3px">a\leq x\leq b,</math>&nbsp; where &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; is the upper function and &nbsp;<math style="vertical-align: -5px">g(x)</math>&nbsp; is the lower function.
 |}