What is the integral of sin^2(1/2 pix) ?

The integral of sin^2(1/2 pix) is 1/2 (x-1/pi sin(pix))+C

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integral of sin^2(1/2 pix)

\int sin^{2} (\frac{1}{2} π x) d x

\frac{1}{2} (x - \frac{1}{π} sin (π x)) + C

Solution steps

\int sin^{2} (\frac{1}{2} π x) d x

Rewrite using trig identities

= \int \frac{1}{2} (1 - cos (π x)) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 - cos (π x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d x - \int cos (π x) d x)

\int 1 d x = x

\int cos (π x) d x = \frac{1}{π} sin (π x)

= \frac{1}{2} (x - \frac{1}{π} sin (π x))

Add a constant to the solution

= \frac{1}{2} (x - \frac{1}{π} sin (π x)) + C

5 ln (x^{2}), x = 1

\int (\frac{9}{x}) d x

\frac{d}{d x} (2 - 7 x)

\frac{d}{d x} (\frac{sin ^{2} ( x )}{sin ( x ^{2} )})

\int_{0}^{π} sec (x) d x

What is the integral of sin^2(1/2 pix) ?
The integral of sin^2(1/2 pix) is 1/2 (x-1/pi sin(pix))+C