Sam A.

asked • 12/22/23

Integrating with Respect to Y to find the Area Between 2 Curves Problem

Goal: Find the area of the region enclosed by y=2.25x and x=4--y2 by integrating with respect to y.


A) First find the y coordinates of the two points where y=2.25x meets x=4--y2

B) Integrate using the formula Sdc g(y)dy, where g(y) = _________

C) Evaluate the definite integral to find the Area


I've had a lot of practice integrating with respect to x to find the area, but I'm really struggling finding resources that show how to integrate with respect to y, instead. Any help is appreciated! Thank you!

1 Expert Answer

By:

Doug C. answered • 12/22/23

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Math Tutor with Reputation to make difficult concepts understandable

Doug C.

Here is an updated Desmos graph showing that it is possible to solve this problem with respect to x, but it gets really ugly. desmos.com/calculator/z0yvokhfa8 Checkout rows 19-24.
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12/22/23

Sam A.

Thank you so much for this walkthrough! Super helpful!
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12/22/23

Doug C.

This version of the graph shows the exact answer which was ascertained by using an online binomial expansion calculator: desmos.com/calculator/922rupxmgn
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12/22/23

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