Grade 12Integral Calculus

Solve the Integral:
∫sinx.sin2xdx

Lovey

11 Years agoGrade 12

2 Answers

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int sinx.sin2xdx$
$I = \int sinx.(2sinx.cosx)dx$
$I = \int 2sin^{2}x.cosxdx$
$sinx = t$
$cosxdx = dt$
$I = \int 2t^{2}dt$
$I = \frac{2t^{3}}{3} + constant$
$I = \frac{2sin^{3}x}{3} + constant$

Sunil Raikwar

11 Years ago

∫sinx.sin2xdx
=∫sinx.2sinxcosxdx
= 2∫sin²x.cosxdx
let t = sinx
dt = cosxdx
∫ t^2 dx = t^3/3 +c = sin³x/3 +c
where c is a constant

Thanks & Regards
Sunil Raikwar
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