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

Question

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

Answer 1

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/x² --> y=1/25

b=4

Area = ∫_1/25⁴|5-1/√y|dy = 5y-2√y|_1/25⁴ = 20-4-1/5+2/5 = 16+1/5 = 81/5

Answer 2

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