What is the integral from 0 to 1 of sin(4pix) ?

The integral from 0 to 1 of sin(4pix) is 0

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integral from 0 to 1 of sin(4pix)

\int_{0}^{1} sin (4 π x) d x

0

Solution steps

\int_{0}^{1} sin (4 π x) d x

Apply u-substitution

: \int_{0}^{4 π} sin (u) \frac{1}{4 π} d u

= \int_{0}^{4 π} sin (u) \frac{1}{4 π} d u

Take the constant out:

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

= \frac{1}{4 π} \cdot \int_{0}^{4 π} sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{4 π} [- cos (u)]_{0}^{4 π}

Compute the boundaries:

0

= \frac{1}{4 π} \cdot 0

Simplify

= 0

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What is the integral from 0 to 1 of sin(4pix) ?
The integral from 0 to 1 of sin(4pix) is 0