SAMPLE QUESTIONS
1. The value of the integral $\int_{-\pi/2}^{\pi/2}\left (x^{2} + ln\frac{\pi + x}{\pi - x} \right )cosx dx$ is
a) 0
b) $\frac{\pi^{2}}{2} - 4$
c) $\frac{\pi^{2}}{2} + 4$
d) $\frac{\pi^{2}}{2}$
2. The area of the region between the curves y = $\sqrt{\frac{1 + sinx}{cosx}}$ and y = $\sqrt{\frac{1 - sinx}{cosx}}$ bounded by the lines x = 0 and x = $\frac{\pi}{4}$ is
a) $\int_{0}^{\sqrt{2}-1}\frac{t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$
b) $\int_{0}^{\sqrt{2}-1}\frac{4t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$
c) $\int_{0}^{\sqrt{2}+1}\frac{4t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$
d) $\int_{0}^{\sqrt{2}+1}\frac{t}{\left (1 + t^{2} \right )\sqrt{1 - t^{2}}}dt$