First slide

Integration

Question

Solve the following Integrals $\int \frac{\cos^{3} θ}{1 - \sin θ} d θ$

Moderate

A

$\sin θ - \frac{\sin^{2} θ}{2} + C$
B

$\sin θ + \frac{\cos^{2} θ}{2} + C$
C

$\cos θ + \frac{\cos^{2} θ}{2} + C$
D

$\sin θ - \frac{\cos^{2} θ}{2} + C$

Solution

$\begin{array}{l} \int \frac{(1 - \sin^{2} θ)}{1 - \sin θ} \cos θ d θ put \sin θ = t; \cos d θ = d t \\ \int (\frac{1 - t^{2}}{1 - t}) d t = \int (1 + t) d t = t + \frac{t^{2}}{2} + c = \sin θ + \frac{\sin^{2} θ}{2} + c \end{array}$

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