## anonymous one year ago Using geometry to calculate a definite integral - I know how to do this generally (calculate the area) but for this question the graph is a semicircle and I have to find the area of part of the semicircle! Not sure how to do this one..

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1. anonymous

$\int\limits_{-0.5}^{0} \sqrt{1-x^2} dx$ this is the definite integral (i made an error in the original post - it's a definite integral that i have to find!)

2. anonymous

|dw:1444175151872:dw| and this is a very rough drawing of what i know the graph looks like - the shaded part is the area i know i need to calculate!

3. anonymous

You can compute the area of the segment (the new shaded region), then subtract it from half the circle's area. |dw:1444175486963:dw|

4. anonymous

... and divide by 2, of course, to only count the red region.

5. anonymous

|dw:1444175617048:dw|

6. anonymous

Thanks so much!