Vinod Singh and Shweta Pawar Solutions for Chapter: Applications of Definite Integral, Exercise 4: Evaluation Test

The area bounded by the curve $x=2-y-y^2$ and the $Y$-axis is

The area of the region bounded by the curve $y^2=4a^2\left(x-1\right)$ and the lines $x=1, y=4a$ is

The area bounded by the curves $y^2=x+1$ and $y^2=-x+1$ is

The area enclosed by the curve $y=x^2+x+1$ and the lines $x=-1, y=0$ and the tangent to the curve at the point $\left(1, 3\right)$ is

The area of the region bounded by the curves $x^2+4y^2=4$ and $4y^2=3x$ is

The slope of the tangent to a curve $y=f\left(x\right)$ at $\left(x, f\left(x\right)\right)$  is $2x+1$. If the curve passes through the point $\left(1,2\right),$ then the area of the region bounded by the curve, the $X-$axis and the line $x=1$ is

The area bounded by $y={\sin }^{-1}x, x=\frac{1}{\sqrt{2}}$ and the $X-$axis is

The area enclosed by the parabola ${\left(y-2\right)}^2=x-1,$ the tangent to the parabola at $\left(2, 3\right)$  and the $X-$axis is