\int 3\sqrt{\frac{\sin^{n}x}{\cos ^{n+6}x}}.dx \,\, n\epsilon N=

  • Option 1)

    \frac{3}{n}(\tan x)^{\frac{n}{3}+1}+c

  • Option 2)

    \frac{3}{3+n}(\tan x)^{\frac{n}{3}+1}+c

  • Option 3)

    \frac{3}{n}(\cos x)^{\frac{n}{3}+1}+c

  • Option 4)

    None of these

 

Answers (1)

As learnt

Integration of trigonometric function of power m -

\int tan^{m}xdx , \int cot^{m}xdx

 

 

- wherein

for m=2

use tan^{2}x=sec^{2}x-1  , cot^{2}x=cosec^{2}x-1

 

 

\int \sqrt{\frac{\sin ^{n}x}{\cos ^{n+6}x}} \: dx \: \: \: = \: \: \int \left [ \frac{\sin ^{n}n}{\cos ^{n}x\cdot \cos ^{6}x} \right ]^{\frac{1}{3}}dx

                               =\int \left ( tan^{n}x \right )^{\frac{1}{3}}\cdot \sec ^{2}xdx

Let

 \\ tanx=t \\ sec^{2}xdx=dt

\int t^{\frac{n}{3}}dt=\frac{3}{n+3}t^{\frac{n}{3}+1}

              =\frac{3}{n+3}(tanx)^{\frac{n}{3}+1}

 


Option 1)

\frac{3}{n}(\tan x)^{\frac{n}{3}+1}+c

This option is incorrect

Option 2)

\frac{3}{3+n}(\tan x)^{\frac{n}{3}+1}+c

This option is correct

Option 3)

\frac{3}{n}(\cos x)^{\frac{n}{3}+1}+c

This option is incorrect

Option 4)

None of these

This option is incorrect

Most Viewed Questions

Preparation Products

Knockout BITSAT 2021

It is an exhaustive preparation module made exclusively for cracking BITSAT..

₹ 4999/- ₹ 2999/-
Buy Now
Knockout BITSAT-JEE Main 2021

An exhaustive E-learning program for the complete preparation of JEE Main and Bitsat.

₹ 27999/- ₹ 11999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions