Evaluate the following integral ∫_0^1(5x^3)/√(1-x^8 ) dx
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total answers (1)
total answers (1)
Mathematics
∫_0^1(5x^3)/√(1-x^8 ) dx put u=x^2→du=4x^3 dx
need an explanation for this answer? contact us directly to get an explanation for this answerI=5∫_0^1du/(4√(1-u^2 )) let u=sinθ→du=cosθ dθ
u=0→θ=0 & u=1 →θ=π/2
∴I=5/4 ∫_0^(π/2)cosθdθ/√(1-〖sin〗^2 θ)=5/4 ∫_0^(π/2 )dθ=5π/8