Can someone please help with the below question?

label Calculus
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Determine the area between the curves f(x)=7x and g(x)=x^2-8

Jul 14th, 2015

Thank you for the opportunity to help you with your question!

We need to find out where they intersect, because those points will be our boundaries for integration.

Set them equal to one another:

7x = x^2 -8

x^2 - 7x - 8 = 0

Factor:

(x-8)(x+1) = 0

x = 8, x = -1

So! We need to subtract one function from the other (in this case, 7x is "on top" so to speak, in the first quadrant):

Integrate from -1 to 8 f(x) - g(x)

I(-1-->8) 7x - (x^2 - 8)

I(-1 --> 8) -x^2 + 7x + 8

I(-1 --> 8) -x^2/2 + 7x^2/2 + 8x

And you end up with 243/2 :)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 14th, 2015

I sent you the $10 promotion code for helping me! Thank you so much!

Jul 15th, 2015

Aw, thank you so much! That was so kind of you, and greatly appreciated by me :D

Jul 15th, 2015

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Jul 14th, 2015
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Jul 14th, 2015
Jun 29th, 2017
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