Area between x=g(y) and y Axis

Q.

If n is any integer, then ${\int }_0^{\pi }{e}^{co{s}^{2}x}co{s}^3(2n+1)xdx=$ [IIT 1985; RPET 1995; UPSEAT 2001]

1. None of these

2. x

3. 1

4. 0

Q. ${\int }_0^{\frac{\pi }{2}}\frac{sinx}{1+cosx+sinx}dx=$

1. $\frac{\pi }{4}$
2. $\frac{\pi }{4}+log\sqrt{2}$
3. $\frac{\pi }{4}-log\sqrt{2}$
4. $\frac{\pi }{4}-log2$

Q.

${\int }_{-1}^{1}x|x|dx=$ [MP PET 1990; Pb. CET 2004]

1. 1
2. 0
3. 2
4. -2

Q. ${\int }_0^{\pi }sin\left(x\right)dx-$

1. $Noneofthese$
2. $2{\int }_0^{\frac{\pi }{2}}sin\left(x\right)dx$
3. $2{\int }_0^{\frac{\pi }{2}}cos\left(x\right)dx$
4. $2{\int }_0^{\pi }sin\left(x\right)dx$

Q. If the area bounded by the graph of $y=x{e}^{-ax}(a>0)$ and the abscissa is $\frac{1}{9}$ sq. unit, then the value of $a$ is equal to

Q.

${\int }_{-1}^{1}log\frac{2-x}{2+x}dx=$ [Roorkee 1986; Kurukshetra CEE 1998]

1. 2
2. 1
3. -1
4. 0

Q. If ${\int }_0^{\frac{\pi }{2}}cos\left(x\right)dx=athen{\int }_0^{\pi }cos\left(x\right)dx$ is equal to -

1. $2a$
2. $a$
3. $a^2$
4. $0$

Q. The area enclosed by the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is equal to

1. ${\pi }^2\mathrm{ab}$
2. $\mathrm{\pi ab}$
3. ${\mathrm{\pi a}}^{2}b$
4. ${\mathrm{\pi ab}}^2$

Q. The area of the region bounded by the curve y = x + 1 and the lines x = 2 and x = 3 is

1. $\frac{7}{2}\mathrm{square}\mathrm{units}$
2. $\frac{9}{2}\mathrm{square}\mathrm{units}$
3. $\frac{11}{2}\mathrm{square}\mathrm{units}$
4. $\frac{13}{2}\mathrm{square}\mathrm{units}$

Q. Find the area of the region bounded by x 2 = 4 y , y = 2, y = 4 and the y -axis in the first quadrant.