Area between Two Curves

Q. ${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}log\left(\frac{2-sin\theta }{2+sin\theta }\right)d\theta =$

1. 0

2. 1

3. 2

4. None of these

Q. The area bounded by the curves $x=y^2$ and $x=3-2y^2$ is

1. 2
2. 4
3. 4/3
4. None of these

Q. ${\int }_{-1}^1{e}^{|x|}dx$

1. e
2. 2e
3. e-1
4. 0.02

Q. ${\int }_{-1}^1{e}^{|x|}dx$

1. 2e
2. 0.02
3. e
4. e-1

Q.

Let f : R $\to$ R and g : R $\to$ R be continuous functions, then the value of the integral ${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\left[f\right(x)+f(-x\left)\right]\left[g\right(x)-g(-x\left)\right]dx=$ [IIT 1990; DCE 2000; MP PET 2001]

1. $\pi$
2. 1
3. 0
4. -1

Q.

If the ordinate $x=a$ divides the area bounded by the curve $y=(1+\frac{8}{x^2}),$ x - axis and the ordinates $x=2,x=4$ into two equal parts, then a =

1. 8

2. 2

3. $2\sqrt{2}$

4. $\sqrt{2}$

Q. The value of ${\int }_0^2\frac{2x^3-6x^2+9x-5}{x^2-2x+5}dx$ equals

1. 4
2. -1
3. None of the above
4. 1

Q. Find the area enclosed between the curve $y=5x-x^{2}andy=x$ .

1. $16$
2. $32$
3. $\frac{32}{3}$
4. $\frac{32}{9}$
   
   

Q. The area bounded by the curves $y=|x|-1$ and $y=-|x|+1$ is

1. $1$
2. $2$
3. $2\sqrt{2}$
4. $4$

Q. ${\int }_{-1}^1{x}^{3}dx$ = ___