Mathematics

# Write a value of $\int { { x }^{ 2 } } \sin { { x }^{ 3 } } dx\quad$

##### SOLUTION
Let $t={x}^{3}\Rightarrow\,dt=3{x}^{2}dx$

$\Rightarrow\,\dfrac{dt}{3}={x}^{2}dx$

$I=\displaystyle\int{{x}^{2}\sin{{x}^{3}}dx}$

$=\displaystyle\int{\sin{t}\dfrac{dt}{3}}$

$=\dfrac{1}{3}\displaystyle\int{\sin{t}dt}$

$=\dfrac{1}{3}\left(-\cos{t}\right)+c$ since $\displaystyle\int{\sin{x}dx}=-\cos{x}+c$

$=-\dfrac{1}{3}\cos{t}+c$    .......where $c$ is the constant of integration

$=-\dfrac{1}{3}\cos{{x}^{3}}+c$ ........where $t={x}^{3}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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