The area of the region, inside the circle ( x − 2 3 ) 2 + y 2 = 12 and outside the parabola y 2 = 2 3 x is :

Question

The area of the region, inside the circle ( x − 2 3 ​ ) 2 + y 2 = 12 and outside the parabola y 2 = 2 3 ​ x is :

TestHub · Accepted Answer

​ Required area = 2 ∫ 0 2 3 ​ ​ ( 4 3 ​ x − x 2 ​ − 2 3 ​ x ​ ) d x = 2 ∫ 0 2 3 ​ ​ ( 12 − ( x − 2 3 ​ ) 2 ​ − 2 3 ​ x ​ ) d x = 2 [ 2 x − 2 3 ​ ​ 12 − ( x − 2 3 ​ ) 2 ​ + 2 12 ​ sin − 1 ( 2 3 ​ x − 2 3 ​ ​ ) − 2 3 ​ 2 3 ​ ​ x 2 3 ​ ​ ] 0 2 3 ​ ​ = 2 { 3 π − 8 } = 6 π − 16 sq. units. ​

Mathematics - Area under the curve Question with Solution | TestHub

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