Evaluate the following integral ∫〖〖sin〗^4 x〗 dx
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total answers (1)
total answers (1)
Mathematics
∫〖〖sin〗^4 x〗 dx=∫(〖sin〗^2 x)^2 dx
need an explanation for this answer? contact us directly to get an explanation for this answer=∫((1-cos2x)/2)^2 dx
=1/4 ∫(1-2cos2x+〖cos〗^2 2 x) dx
=1/4 (x-sin2x)+1/4 ∫(1+cos4x)/2 dx
=x/4-1/4 sin2x+1/8 (x+1/4 sin4x)+C
=3/8 x-1/4 sin2x+1/32 sin4x+C