Mathematics

Evaluate the following integrals:

$$\int { \sin ^{ 5 }{ x } \cos ^{  }{ x }  } dx$$


SOLUTION
$$I=\displaystyle\int{{\sin}^{5}{x}\cos{x}dx}$$

Let 

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

$$I=\displaystyle\int{{t}^{5}\,dt}$$

$$=\dfrac{1}{6}{t}^{6}+c$$ where $$c$$ is the constant of integration.

$$=\dfrac{1}{6}{\sin}^{6}{x}+c$$ 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 Medium
The value $$\displaystyle\int_{-10}^{10}\frac{dx}{e^{x^{5}}+1}$$ of is equal to?
  • A. $$20$$
  • B. $$e^{10^{5}}+1$$
  • C. $$\displaystyle\frac{e^{10^{5}}+1}{e^{10^{5}}}$$
  • D. $$10$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Integrate the function    $$\displaystyle \frac {\sec^2x}{\sqrt {\tan^2x+4}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
$$\displaystyle\int {{{dx} \over {\sqrt {{{\sin }^3}x\cos x} }} = g(x)}  + c \Rightarrow g(x) = $$
  • A. $$\displaystyle{2 \over {\sqrt {\cot x} }}$$
  • B. $$\displaystyle{2 \over {\sqrt {\tan x} }}$$
  • C. $$\displaystyle{1 \over {\sqrt {\cot x} }}$$
  • D. $$\displaystyle{{ - 2} \over {\sqrt {\tan x} }}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
$$\displaystyle \int_{2}^{8}\dfrac {\sqrt {10-x}}{\sqrt {x}+\sqrt {10-x}}dx$$ is
  • A. $$2$$
  • B. $$3$$
  • C. $$4$$
  • D. $$1$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Let $$\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$$

Then answer the following question.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer