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

The integral of sin^2(2pix) is 1/2 (x-1/(4pi)sin(4pix))+C

Popular >

integral of sin^2(2pix)

\int sin^{2} (2 π x) d x

\frac{1}{2} (x - \frac{1}{4 π} sin (4 π x)) + C

Solution steps

\int sin^{2} (2 π x) d x

Rewrite using trig identities

= \int \frac{1}{2} (1 - cos (4 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 (4 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 (4 π x) d x)

\int 1 d x = x

\int cos (4 π x) d x = \frac{1}{4 π} sin (4 π x)

= \frac{1}{2} (x - \frac{1}{4 π} sin (4 π x))

Add a constant to the solution

= \frac{1}{2} (x - \frac{1}{4 π} sin (4 π x)) + C

x \to - 2 lim (\frac{x - 2}{∣ x - 2 ∣})

x \to 0 lim (\frac{cos ( π x )}{x})

t e^{- 3 t}

\frac{d}{d x} ((x^{3} - 1)^{100})

y = x^{4}, x = y^{7}, 1

What is the integral of sin^2(2pix) ?
The integral of sin^2(2pix) is 1/2 (x-1/(4pi)sin(4pix))+C