A farmer F 1 has a land in the shape of a triangle with vertices at P ( 0, 0 ) , Q ( 1, 1 ) and R ( 2, 0 ) . From this land, a neighbouring farmer F 2 takes away the region which lies between the side P Q and a curve of the form y = x n ,   n > 1 . If the area of the region taken away by…

Question

A farmer F 1 has a land in the shape of a triangle with vertices at P ( 0, 0 ) , Q ( 1, 1 ) and R ( 2, 0 ) . From this land, a neighbouring farmer F 2 takes away the region which lies between the side P Q and a curve of the form y = x n , &#160; n &#62; 1 . If the area of the region taken away by the farmer F 2 is exactly 30% of the area of &#8710; P Q R , then the value of n is

Aicharya · Accepted Answer

Area = ∫ 0 1 x - x n d x = 3 10 x 2 2 - x n + 1 n + 1 0 1 = 3 10 1 2 - 1 n + 1 = 3 10 ∴ n + 1 = 5 ⇒ n = 4

A farmer F 1 has a land in the shape of a triangle with vertices at P ( 0, 0 ) , Q ( 1, 1 ) and R ( 2, 0 ) .…

Solution