Amit M Agarwal Solutions for Chapter: Area Bounded by Curves, Exercise 3: Target Exercises

The area bounded by the curves $\sqrt{x}+\sqrt{y}=1$ and $x+y=1$, is

The area of the region bounded by $y=\left|\left[x-2\right]\right|$, $X$-axis and the lines $x=-1$ and $x=2,$ where $\left[·\right]$ denotes greatest integer function, is

The area of the triangle formed by the lines $y=2x, x=0$ and $y=2$, is

The area of the smaller portion of the circle $x^2+y^2=a^2, a>0$ cut-off by the line $x=\frac{a}{2}$ is

If the curve $y=x^2-7x+10$ intersect $X$-axis at the points $A$ and $B$, then the area bounded by the curve and the line $AB$ is

If $f\left(x\right)=a+bx+c{x}^2$, where $c>0$ and $b^2-4ac<0,$ then the area enclosed by the coordinate axes, the line $x=2$ and the curve $y=f\left(x\right)$, is given by

The area bounded by the curve $\sqrt{\left|x\right|}+\sqrt{\left|y\right|}=\sqrt{a}$ and $x^2+y^2=a^2, a>0$, is

A curve $y=f\left(x\right)$ passes through the point $P\left(1,1\right)$, the normal to the curve at $P$ is $a\left(y-1\right)+\left(x-1\right)=0$. If the slope of the tangent at any point on the curve $y=e^{a(x-1)}$ is proportional to the ordinate of that point, then the area bounded by $Y$-axis, the curve and the normal to the curve at $P$, is