Fel R.

asked • 08/04/21# Find the area of the region bounded by y=1/x^2,y-4, and x=5. Use dy to integrate and/or differntiate.

In this question find the area but use dy to set up the integral and bounds.

## 2 Answers By Expert Tutors

Area = ∫_{a}^{b}|f(y)-g(y)|dy

f(y) = right boundary =5

g(y) = left boundary = y^{-1/2}

a is the intersection at x=5 and y=1/x^{2} --> y=1/25

b=4

Area = ∫_{1/25}^{4}|5-1/√y|dy = 5y-2√y|_{1/25}^{4} = 20-4-1/5+2/5 = 16+1/5 = 81/5

Miles K. answered • 08/04/21

Patient and Passionate STEM Tutor, Engineer

Oops! I said errors are a great way to learn, and then I forgot to explain how I found mine. When I first solved the problem, I got an area that was less than half the total area of the bounding box (4.5 x 4 = 18 square units), when a clear visual inspection shows us that the area in question is much greater than half of that.

Hope this helps!

-Miles

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William W.

y=1/x^2 needs to be bounded on the left as well as right, the bottom as well as the top. y = 4 (you have listed "y-4") is the top. Is the bottom the x-axis? x = 5 is the right, is the left the y-axis?08/04/21