Mathematics

# Write a value of $\int { \sin ^{ 3 }{ x } \cos { x } dx }$

##### SOLUTION
Let $t=\sin{x}\Rightarrow\,dt=\cos{x}dx$

$I=\displaystyle\int{{\sin}^{3}{x}\cos{x}dx}$

$=\displaystyle\int{{t}^{3}dt}$

$=\dfrac{{t}^{4}}{4}+c$   .....where $c$ is the constant of integration.

$=\dfrac{{\sin}^{4}{x}}{4}+c$    .......where $t=\sin{x}$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Hard
$\int \frac { x ^ { 2 } } { \left( x ^ { 2 } + 2 \right) \left( x ^ { 2 } + 3 \right) } d x =$
• A. $- \sqrt { 2 } \tan ^ { - 1 } x + \sqrt { 3 } \tan ^ { 1 } x + c$
• B. $\sqrt { 2 } \tan ^ { - 1 } \left( \frac { x } { \sqrt { 2 } } \right) + \sqrt { 3 } \tan ^ { - 1 } \left( \frac { x } { \sqrt { 3 } } \right) + c$
• C. None of these
• D. $- \sqrt { 2 } \tan ^ { - 1 } \left( \frac { x } { \sqrt { 2 } } \right) + \sqrt { 3 } \tan ^ { - 1 } \left( \frac { x } { \sqrt { 3 } } \right) + c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate $\displaystyle \int {\dfrac {y(1+y)}{1-y}}dy$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate:
$\displaystyle\int^{\pi /2}_0\dfrac{\sin x \cos x}{(2\sin x+1)(\sin x+1)}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int \frac{cosec x}{\log \tan \left ( x/2 \right )}dx$
• A. $\displaystyle \log \left [ \log \tan \left ( x \right ) \right ].$
• B. $\displaystyle \log \left [ \log \cot \left ( x/2 \right ) \right ].$
• C. $\displaystyle \log \left [ \log \cot \left ( x \right ) \right ].$
• D. $\displaystyle \log \left [ \log \tan \left ( x/2 \right ) \right ].$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
Evaluate: $\displaystyle \int { \dfrac { \cos { x } -\sin { x } }{ 1+\sin { 2x } } } dx$
• A. $\dfrac{1}{\sin x+\cos x}+C$
• B. $\dfrac{2}{\sin 2x+\cos x}+C$
• C. $-\dfrac{2}{\sin 2x+\cos x}+C$
• D. $-\dfrac{1}{\sin x+\cos x}+C$