Mathematics

Evaluate:
$$\int { \sin ^{ 4 }{ x }  } \cos ^{ 3 }{ x } .dx$$


SOLUTION
$$2sinccosD=sin\left\{ C-D \right\} +sin\left\{ C+D \right\} $$
$$\int { sin4xcos3xdx=\int { \frac { 1 }{ 2 } \left[ sin\left\{ 4x-3x \right\} +sin\left\{ 4x+3x \right\}  \right]  } dx } $$
$$\frac { 1 }{ 2 } \int { \left[ sinx+sin7x \right] dx } $$
$$\frac { 1 }{ 2 } \left[ -cosx-\frac { cos7x }{ 7 }  \right] C$$
$$-\frac { 1 }{ 2 } cosx-\frac { 1 }{ 14 } cos7x+C$$
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Subjective Hard Published on 17th 09, 2020
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