Embibe Experts Solutions for Chapter: Area under Curves, Exercise 1: EXERCISE-1

The area of the figure bounded by the curves  $y=\ln x$ and $y={\left(\ln x\right)}^2$ is -

The area of the closed figure bounded by $y=x, y=-x$ and the tangent to the curve $y=\sqrt{x^2-5}$ at the point $\left(3, 2\right)$ is

The area (in sq. units) of the region(s) enclosed by the curves $y=x^2$ and $y=\sqrt{\left|x\right|}$ is

The area enclosed by the curves $y=\cos x, y=1+\sin 2x$ and $x=\frac{3\pi }{2}$ as $x$ varies from $0$ to $\frac{3\pi }{2},$ is - 

The area of the region for which $0<y<3-2x-x^2$ and $x>0$ is - 

The area bounded by the curves $y=x\left(1-\ln x\right)$ and positive $x$-axis between $x=e^{-1}$ and $x=e$ is - 

The curve $f\left(x\right)=A{x}^2+Bx+C$ passes through the point $\left(1, 3\right)$ and line $4x+y=8$ is tangent to it at the point $(2, 0)$. The area enclosed by $y=f\left(x\right)$, the tangent line and the $y$-axis is -

Let $y=g\left(x\right)$ be the inverse of a bijective mapping $f:R\to R$, where $f\left(x\right)=3x^3+2x$. The area bounded by graph of $g\left(x\right),$ the $x$-axis and the ordinate at $x=5$ is -