Evaluate the following integral ∫_0^(π⁄2)〖〖sin〗^8 x〗 dx ,∫_0^(π⁄2)〖〖cos〗^7 x〗 dx
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total answers (1)
total answers (1)
Mathematics
Since:
need an explanation for this answer? contact us directly to get an explanation for this answer∫_0^(π⁄2)〖〖sin〗^n x〗 dx=∫_0^(π⁄2)〖〖cos〗^n x〗 dx=((n-1)(n-3)(n-5)…)/(n(n-2)(n-4)…)*{(π⁄2 ,n even2⁄3 , n odd)┤
∴∫_0^(π⁄2)〖〖sin〗^8 x〗 dx=7.5.3/8.6.4.2*π/2=105/384*π/2
∫_0^(π⁄2)〖〖cos〗^7 x〗 dx=6.4.2/7.5.3.1*1=48/105