Basic maths-calculus-Q5

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The value of the integral \int_{\pi/6}^{5\pi/6} sin^3x cos^5x \text{ dx}  is ____?

asked May 19 in Basic Maths by gbeditor (44,500 points)
reshown May 24 by gbeditor

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We know the following property of definite integral :

For the given question, f(x) = sin^3x cos^5x

a = \pi/6; b = 5\pi/6

f(a+b-x) = -sin^3x cos^5x   (because sin(\pi - x) = sinx ; cos(\pi - x) = -cosx )

Let the given intergral equation be L, then we have L = -L; 

2L = 0

L = 0

answered May 27 by deepak-gatebook (112,390 points)
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