Mathematics

# Find the integral of the function$\sin 4x\sin 8x$

##### SOLUTION

Consider the given function.

$I=\int{\sin 4x\sin 8xdx}$

$I=\int{\sin 4x\sin 2\left( 4x \right)dx}$

$I=\int{\sin 4x\left( 2\sin 4x\cos 4x \right)dx}$

$I=2\int{{{\sin }^{2}}4x\cos 4xdx}$

Let $t=\sin 4x$

$\dfrac{dt}{dx}=4\cos 4x$

$\dfrac{dt}{4}=\cos 4xdx$

Therefore,

$I=\dfrac{2}{4}\int{{{t}^{2}}dt}$

$I=\dfrac{1}{2}\left[ \dfrac{{{t}^{3}}}{3} \right]+C$

$I=\left[ \dfrac{{{t}^{3}}}{6} \right]+C$

On putting the value of $t$, we get

$I=\dfrac{{{\sin }^{3}}4x}{6}+C$

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
$\displaystyle \int \frac{dx}{x^2(x^5+1)^{\frac{4}{5}}}$ equals :

• A. $\displaystyle c+\frac{\sqrt[5]{1+x^5}}{4x}$
• B. $\displaystyle c-\frac{\sqrt[5]{1+x^5}}{5x}$
• C. $\displaystyle c+\frac{\sqrt[5]{1+x^5}}{x}$
• D. $\displaystyle c-\frac{\sqrt[5]{1+x^5}}{x}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int ^{\displaystyle \frac{3 \pi}{10}}_{\displaystyle \frac{\pi}{5}} \frac{sin x}{sin x + cos x}dx$ is equal to
• A. $\pi$
• B. $\displaystyle \frac{\pi}{2}$
• C. $\displaystyle \frac{\pi}{4}$
• D. $\displaystyle \frac{\pi}{20}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int_{-2}^{2} |x \,cos \,\pi x| dx$ is equal to
• A. $\dfrac{4}{\pi}$
• B. $\dfrac{2}{\pi}$
• C. $\dfrac{1}{\pi}$
• D. $\dfrac{8}{\pi}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\int {\dfrac{{dx}}{{\sqrt {x + 1} \, - \sqrt x }}}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \int e^{x}\sqrt{1+e^{x}}dx=$
• A. $(1+e^{x})^{\frac{3}{2}}+c$
• B. $\displaystyle \frac{2}{3}(1-e^{x})^{3/{2}}+c$
• C. $(1-e^{x})^{3/{2}}+c$
• D. $\displaystyle \frac{2}{3}(1+e^{x})^{3/{2}}+c$