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

The integral from 0 to 1 of sin(pit) is 2/pi

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integral from 0 to 1 of sin(pit)

\int_{0}^{1} sin (π t) d t

\frac{2}{π}

Decimal

0.63661 \dots

Solution steps

\int_{0}^{1} sin (π t) d t

Apply u-substitution

= \int_{0}^{π} 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} sin (u) d u

Use the common integral:

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

= \frac{1}{π} [- cos (u)]_{0}^{π}

Compute the boundaries:

2

= \frac{1}{π} \cdot 2

Simplify

= \frac{2}{π}

\frac{d}{d x} (- 4 x^{3} + 4 x)

\int c (x) d x

d er i v a t i v e h (x) = [\frac{x + 1}{x - 1}]^{3}

\frac{\partial}{\partial x} ((\frac{y}{z})^{\frac{1}{x}})

y^{^{''}} + 3 y = 48 x^{2} e^{3 x}

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