Area between x=g(y) and y Axis

Q.

Why are $\cos \left(\mathrm{\pi }\right)$ and $\cos \left(-\mathrm{\pi }\right)$ both equal to $-1$?

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. x

2. 1

3. 0

4. None of these

Q.

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

1. 2
2. 1
3. -1
4. \N

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.

${\int }_{-1}^1{x}^{17}co{s}^{4}xdx=$ [MP PET 1990]

1. -2
2. -1
3. \N
4. 2