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Formula
Calculate the integral
Answer
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$\int{ \left( \sin\left( x \right) \right) ^{ 2 } }d{ x }$
$\dfrac { 1 } { 2 } \left ( - \cos\left( x \right) \sin\left( x \right) + x \right )$
Calculate the integral
$\displaystyle\int { \color{#FF6800}{ \sin ^ { 2 } \left ( x \right) } } d { \color{#FF6800}{ x } }$
$ $ Calculate the integral using the formula of $ \int \sin^{n}(x) dx = - \frac{1}{n} \cos(x) \sin^{n-1}(x) + \frac{n-1}{n} \int \sin^{n-2}(x) dx$
$\color{#FF6800}{ \dfrac { 1 } { 2 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \cos\left( x \right) } \color{#FF6800}{ \sin\left( x \right) } \color{#FF6800}{ + } \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } } \right )$
$\dfrac { 1 } { 2 } \left ( - \cos\left( x \right) \sin\left( x \right) + \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } } \right )$
$ $ The indefinite integral of $ 1 $ is $ x $ . $ $
$\dfrac { 1 } { 2 } \left ( - \cos\left( x \right) \sin\left( x \right) + \color{#FF6800}{ x } \right )$
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