Mathematics

# If $f(x) = \int_{0}^{x} t\sin t \ dt$, write the value of $f(x)$

##### SOLUTION
$\int _{ 0 }^{ x }{ t\sin t\quad dt }$
Integrating by parts,
$\Rightarrow $$\int { uv } =uv'-\int { v'\int { u } du } u=t v= sin t \Rightarrow$$t\int { sin t\ dt-\int { \sin t\ dt.\dfrac { d(t) }{ dt } } }$
$\Rightarrow $${ \left[ t\left( - \cos t \right) \right] }_{ 0 }^{ x }-{ \left[ \int { -\cos t dt } \right] }_{ 0 }^{ x } \Rightarrow$${ \left[ -t \cos t \right] }_{ 0 }^{ x }+{ \left[ \sin t \right] }_{ 0 }^{ x }$
$\Rightarrow $$-x\cos x-(-0)+\sin x-\sin 0 \Rightarrow$$-x\cos x+\sin x$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 124

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