Please solve this∫sin3x.cos2x dxLimit is from -1 to 1

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Grade 12Integral Calculus

Please solve this
∫sin³x.cos²x dx
Limit is from -1 to 1

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

Approved Tutor Answer11 Years ago

Ans:Hello student, please find answer to your question
$I = \int_{-1}^{1}sin^{3}x.cos^{2}x dx$
$\int_{-a}^{a}f(x) dx = \int_{0}^{a}[f(x) + f(-x)]dx$
$I = \int_{0}^{1}[sin^{3}x.cos^{2}x+(sin(-x))^{3}(cos(-x))^{2}] dx$
$I = \int_{0}^{1}[sin^{3}x.cos^{2}x+(-sin(x))^{3}(cos(x))^{2}] dx$
$I = \int_{0}^{1}[sin^{3}x.cos^{2}x-sin(x))^{3}.cos(x)^{2}] dx$
$I = \int_{0}^{1}0 dx = 0$