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Please solve this ∫sin 3 x.cos 2 x dx Limit is from -1 to 1

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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

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