SOLUTION: Please help me solve this equation: Sketch the regions enclosed by the given curves and then find the area of the regions. a. {{{ y=e^x }}} {{{ y=(x-1)^2 }}} and {{{ x=2 }}}

Question 350018: Please help me solve this equation: Sketch the regions enclosed by the given curves and then find the area of the regions.
a. and
b. and
c. and
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Find the intersection point between and

So then the area would be,

Expand the terms, integrate, and simplify to get the final answer.
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.
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Same procedure.
Find the two intersection points and by solving,

Proceed as above integrating from one intersection point to the other.

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I'm not sure if the first function is or
If it's , then the integration is straightforward since

Integrating that over to would give you
If it's , then find the intersection point again where,

Then you have to modify the area because at this point the functions cross.

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