What is the integral from 0 to 3 of sin(pix) ?

The integral from 0 to 3 of sin(pix) is 2/pi

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integral from 0 to 3 of sin(pix)

\int_{0}^{3} sin (π x) d x

\frac{2}{π}

Decimal Notation

0.63661 \dots

Solution steps

\int_{0}^{3} sin (π x) d x

Apply u-substitution

: \int_{0}^{π 3} sin (u) \frac{1}{π} d u

= \int_{0}^{π 3} sin (u) \frac{1}{π} d u

Take the constant out:

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

= \frac{1}{π} \cdot \int_{0}^{π 3} sin (u) d u

Use the common integral:

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

= \frac{1}{π} [- cos (u)]_{0}^{π 3}

Compute the boundaries:

2

= \frac{1}{π} \cdot 2

Simplify

= \frac{2}{π}

\frac{d}{d x} (a x^{3} + b x^{2} + c)

\int (r^{3} + 2 r) d r

x^{2} - 4 x, - x^{2} + 6 x

\frac{d y}{d x} = e^{2 x} - 3 y, y (0) = 1

4 sec (x) - 8 cos (x)

What is the integral from 0 to 3 of sin(pix) ?
The integral from 0 to 3 of sin(pix) is 2/pi