Question

integration of sin5x cos3x dx if lower limit is zero and upper limit is pi/2​

Answer 1

Answer:

${\large{\boxed {\boxed {\boxed { \ { 0.0417 { {\ { }}} }} }}}}$

Step-by-step explanation:

$\int_{0}^{\pi/2} sin^2\times cos^3\times dx$

using Wallis formula:

$\int_{0}^{\pi/2} sin^m\times cos^n\times dx =\frac{(m-1)(m-3)(m-5)...1(n-1)(n-3)(n-5)..1}{(m+n(m+n-2(m+n-4)...1}.\alpha$

In this problem; m=5 ; n=3 ; a = 1 ,since both m and n are odd numbers

$\int_{0}^{\pi/2} sin^5\times cos^3\times dx =\frac{{(5-1)(5-3)(3-1)} }{8(6)(4)(2)} .1\\\\\int_{0}^{\pi/2} sin^5\times cos^3\times dx =\frac{{4(2)(2)} }{8(12)} .1\\\\\int_{0}^{\pi/2} sin^5\times cos^3\times dx =\frac{{4(4)} }{8(12)} .1\\\\\\\int_{0}^{\pi/2} sin^5\times cos^3\times dx =\frac{{16} }{96} .1\\\\\int_{0}^{\pi/2} sin^5\times cos^3\times dx =0.0417$

${\large{\boxed {\boxed {\boxed { \ { 0.0417 { {\ { }}} }} }}}}$

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Answer 2

Answer:

0=0478

Step-by-step explanation:

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