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 $$t=\sin{x}$$
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

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. $$- \sqrt { 2 } \tan ^ { - 1 } \left( \frac { x } { \sqrt { 2 } } \right) + \sqrt { 3 } \tan ^ { - 1 } \left( \frac { x } { \sqrt { 3 } } \right) + c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$\displaystyle \log \left [ \log \tan \left ( x/2 \right ) \right ].$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$-\dfrac{1}{\sin x+\cos x}+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer