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Grade 12Integral Calculus

Solve
∫|sin2pix| dx
Limit is from 0 to 1.

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

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

$I = \int_{0}^{1}|sin2\pi x|dx$
Period of this function is ½.
$I = 2\int_{0}^{1/2}|sin2\pi x|dx$
And it is +ve b/w 0 and ½.
$I = 2\int_{0}^{1/2}(sin2\pi x)dx$
$I = 2(\frac{-cos2\pi x}{2\pi })_{0}^{1/2}$
$I = (\frac{-cos2\pi x}{\pi })_{0}^{1/2}$
$I = \frac{2}{\pi }$

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