If ∫dx / [√(sin3 x cos x)] = g (x) + c, then g (x) =

1) – 2 / (√cot x)

2) – 2 / √tan x

3) 2 / √cot x

4) 2 / √tan x

Solution: (2) – 2 / √tan x

\(\begin{array}{l}\begin{aligned} \int \frac{d x}{\sqrt{\sin ^{3} x \cos x}} &=\int \frac{\operatorname{cosec}^{2} x}{\operatorname{cosec}^{2} x \sqrt{\sin ^{3} x \cos x}} \\ &=\int \frac{\operatorname{cosec}^{2} x d x}{\sqrt{\operatorname{cosec}^{4} x \sin ^{3} x \cos x}} \\ &=\int \frac{\operatorname{cosec}^{2} x d x}{\sqrt{\cot x}} \\ \text { Let } \cot x=t^{2} & \\ -\operatorname{cosec}^{2} x d x &=2 t d t \\ &=-\int \frac{2 t d t}{t}=-2 \int d t=-2 t+c \\ &=-2 \sqrt{\cot x}+c \\ &=-\frac{2}{\sqrt{\tan x}}+c \end{aligned}\end{array} \)

Was this answer helpful?

 
   

4.5 (2)

(5)
(0)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

Ask
Question