The area of the region x , y : x - 1 ≤ y ≤ 5 - x 2 is equal to

Step-by-step solution

Plotting region for x - 1 ≤ y ≤ 5 - x 2 , we get, The intersection points of the curves x 2 + y 2 = 5 and y = x - 1 will be - 1 , 2   &   2 , 1 Here chord A B subtends a right angle at the centre of the circle. So, required area = area of ∆ A B C + area of segment of circle on chord A B = 1 2 A C · B C + [area of quarter circle - area of ∆ A O B ] = 1 2 × 2 × 2 2 + 90 ° 360 ° × π 5 2 - 1 2 × 5 2 = 5 π 4 - 1 2