# Thread: Using definite integrals to represent area

1. ## Using definite integrals to represent area

Hi I am very confused about this problem:

The question is asking to come up with a Riemann sum, then a definite integral to represent the area of the region shown using the strip method. I'm very confused about what my limits should be for the definite integral and am unsure how to go about solving this... Thank you!

2. ## Re: Using definite integrals to represent area

It seems that you are doing it in terms of y. This is the area of a quarter of a circle in the first quadrant, so for y, the value should go from 0 to √10.
We also have to express the function in terms of x:
x^2+y^2=10, x^2=10-y^2 so f(y)=√(10-y^2)
The area using definite integral, then, should be A = (lim n->∞) (√10 /n) Σ (i=0~n) f(<√10>/n * i).

I hope I'm right...?