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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 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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