What is the integral from 0 to 1/4 of sin^2(pi)x ?

The integral from 0 to 1/4 of sin^2(pi)x is 0

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integral from 0 to 1/4 of sin^2(pi)x

\int_{0}^{\frac{1}{4}} sin^{2} (π) x d x

0

Solution steps

\int_{0}^{\frac{1}{4}} sin^{2} (π) x d x

sin^{2} (π) x = 0

= \int_{0}^{\frac{1}{4}} 0 d x

Integral of a constant:

\int a d x = a x

= [0 \cdot x]_{0}^{\frac{1}{4}}

Simplify

= [0]_{0}^{\frac{1}{4}}

Compute the boundaries:

0

= 0

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\int_{0}^{2} \frac{3}{2} (1 - x)^{2} d x

\int_{0}^{x} 6 (1 - y) d y

\int_{0}^{2} x (x - 2) d x

\int_{0}^{4} (4 x^{2} + x^{\frac{3}{2}}) d x

What is the integral from 0 to 1/4 of sin^2(pi)x ?
The integral from 0 to 1/4 of sin^2(pi)x is 0