Question 37

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Jambmaths question: 

Find the value of $\int_{0}^{\pi }{\frac{{{\cos }^{2}}\theta -1}{{{\sin }^{2}}\theta }d\theta }$ 

Option A: 

$\pi$

Option B: 

$\tfrac{\pi }{2}$

Option C: 

$-\tfrac{\pi }{2}$

Option D: 

$-\pi$

Jamb Maths Solution: 

$\begin{align}  & \int_{0}^{\pi }{\frac{{{\cos }^{2}}\theta -1}{{{\sin }^{2}}\theta }d\theta }=\int_{0}^{\pi }{\frac{{{\sin }^{2}}\theta }{{{\sin }^{2}}\theta }d\theta } \\ & =\int_{0}^{\pi }{d\theta } \\ & =\left[ \theta  \right]_{0}^{\pi }=\pi -0=\pi  \end{align}$

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