First slide

Introduction to integration

Question

$f (x) = \int \frac{d x}{\sin^{4} x}$ is a

Easy

A

Polynomial of degree 3 in $c o t x$
B

Polynomial of degree 4 in $c o t x$
C

Polynomial of degree 4 in $\sin x$
D

Polynomial of degree 3 in $\tan x$

Solution

$\begin{array}{l} f (x) = \int (1 + \cot^{2} x) {cosec}^{2} x d x \\ = - (\cot x + \frac{1}{3} \cot^{3} x) + C \end{array}$
which is polynomial of degree 3 .

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