Area of curves in the first quadrant  TOPIC_SOLVED

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Area of curves in the first quadrant

Postby kotsumu on Fri Jan 28, 2011 5:01 am

I am having problems with this question. I'm not sure how to start and approach this question.

Find the area of the region in the first quadrant that is bounded above by the curve y = e^(3x), below by the curve y = e^x, and on the right by the line x = ln(5).

I know I have to integrate e^x to find the area below the curve y = e^x, but how to find the area above y = e^(3x)? and I'm not sure what the limits are to integrate?

Basically I'm stuck at the beginning...
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Postby stapel_eliz on Fri Jan 28, 2011 12:24 pm

kotsumu wrote:I know I have to integrate e^x to find the area below the curve y = e^x, but how to find the area above y = e^(3x)? and I'm not sure what the limits are to integrate?

Ouch! They were supposed to have mentioned this stuff in class before assigning homework on it! :shock:

To learn the terms and techniques, please try this lesson from Paul's Online Math Notes and also this one from Karl's Calculus Tutor.

Long story short: Subtract the bottom curve from the top curve to find the "height", and integrate between the endpoints (being either points you are given or else the intersection points). :wink:
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Re: Area of curves in the first quadrant

Postby kotsumu on Wed Feb 02, 2011 5:15 am

Thanks! I actually got the problem right. Thanks for the link and explanation!
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