Will you try to integrate?

Level 1

Evaluate ∫ 0 π 2 sin ⁡ 5 x cos ⁡ 2 x d x \displaystyle\int_{0}^{\frac{\pi}{2}} \sin^{5}x \cos^{2}x dx

8 105 \frac{8}{105} 28 35 \frac{28}{35} 8 15 \frac{8}{15} 3 5 \frac{3}{5}

Samuel Ayinde by samuel ayinde , 24, Nigeria

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1 solution

I guess one really easy way to solve such questions is to use the formula :

∫ 0 π 2 sin ⁡ m x cos ⁡ 2 n x d x = Γ ( m + 1 2 ) Γ ( n + 1 2 ) 2 Γ ( m + n + 2 2 ) \displaystyle \int_{0}^{\frac{\pi}{2}} \sin^{m}x \cos^{2n}x dx = \displaystyle \dfrac{\Gamma \left ( \dfrac{m+1}{2}\right ) \Gamma \left ( \dfrac{n+1}{2}\right ) }{2\Gamma \left ( \dfrac{m+n+2}{2}\right )}

Input the values of m = 5 , n = 2 m=5,n=2 and Voila!

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Wow. Nice solution.

I guess we can also use reduction formulae.

samuel ayinde - 6 years, 2 months ago

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