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Grade 12Integral Calculus

Integrate from 0 to 1.
∫|sin2(pi)x| dx
|| is a modulus function.

Lovey

11 Years agoGrade 12

1 Answer

Jitender Singh

Approved Tutor Answer11 Years ago

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

$I = \int_{0}^{1}|sin(2\pi )x|dx$
$I = \int_{0}^{\frac{1}{2}}(sin(2\pi )x)dx+\int_{1/2}^{1}(-sin(2\pi x))dx$
$I = \frac{-cos(2\pi x)}{2\pi }|_{0}^{1/2} + \frac{cos(2\pi x)}{2\pi }|_{1/2}^{1}$
$I = \frac{2}{2\pi } + \frac{2}{2\pi }$
$I = \frac{4}{2\pi } = \frac{2}{\pi }$

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