Question

Evaluate: $\int\limits^{2\pi}_0 {e^{x}\cdotp\sin( \frac{\pi}{4}+ \frac{x}{2})} \, dx$

Answer 1

Dear Student,
ρℓєαѕє мαяк мє вяαιи ℓιѕт !!
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−−(1)Using property of definite integral:I(x)=I(−1+1−x)=I(−x)=∫1−1(sin3(−x).cos2(−x)) dx=∫1−1(−sin3(x).cos2(x)) dx −−−(2)Adding 1 and 2,2I=∫1−1(−sin3(x).cos2(x)+sin3(x).cos2(x)) dx 2I=∫1−1cos2(x)(sin3(x)−sin3(x))dx2I=∫1−1cos2(x).0I=0Hint : Solve remaining questions using this concept

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