Evaluate the Following Integral $$\int _ { y } ^ { \frac { \pi } { 5 } } \sin ^ { 3 } x \cos y d x$$

question 38

Multiple Choice

Evaluate the following integral. $$\int _ { y } ^ { \frac { \pi } { 5 } } \sin ^ { 3 } x \cos y d x$$

• A) \(\frac { \cos y } { 3 } \left( \cos ^ { 3 } \left( \frac { \pi } { 5 } \right) - 3 \cos \left( \frac { \pi } { 5 } \right) + \cos ^ { 3 } ( y ) - 3 \cos ( y ) \right)\)
• B) \(\frac { \cos y } { 12 } \left( \cos ^ { 3 } \left( \frac { \pi } { 5 } \right) - 3 \cos \left( \frac { \pi } { 5 } \right) - \cos ^ { 3 } ( y ) + 3 \cos ( y ) \right)\)
• C) \(\frac { \cos y } { 3 } \left( \cos ^ { 3 } \left( \frac { \pi } { 5 } \right) - \cos \left( \frac { \pi } { 5 } \right) - \cos ^ { 3 } ( y ) + \cos ( y ) \right)\)
• D) \(\frac { \cos y } { 3 } \left( \cos ^ { 3 } \left( \frac { \pi } { 5 } \right) - 3 \cos \left( \frac { \pi } { 5 } \right) - \cos ^ { 3 } ( y ) + 3 \cos ( y ) \right)\)
• E) \(\frac { \cos y } { 3 } \left( \cos ^ { 3 } \left( \frac { \pi } { 5 } \right) - 3 \cos \left( \frac { \pi } { 5 } \right) - \cos ^ { 3 } ( y ) - 3 \cos ( y ) \right)\)

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