If ∫ 0 2 2 x - 2 x - x 2 d x = ∫ 0 1 1 - 1 - y 2 - y 2 2 d y + ∫ 1 2 2 - y 2 2 d y + I ,…

1. ${\int }_0^1\left(1+\sqrt{1-y^2}\right)dy$
2. ${\int }_0^1\left(\frac{y^2}{2}-\sqrt{1-y^2}+1\right)dy$
3. ${\int }_0^1\left(1-\sqrt{1-y^2}\right)dy$
4. ${\int }_0^1\left(\frac{y^2}{2}+\sqrt{1-y^2}+1\right)dy$

Solution

Asked in: JEE Main 2022 (29 Jun Shift 2)

Practice more Definite Integration questions on Aicharya