What is the integral from 0 to 1 of cos((piθ)/2) ?

The integral from 0 to 1 of cos((piθ)/2) is 2/pi

Popular >

integral from 0 to 1 of cos((piθ)/2)

\int_{0}^{1} cos (\frac{π θ}{2}) d θ

\frac{2}{π}

Decimal

0.63661 \dots

Solution steps

\int_{0}^{1} cos (\frac{π θ}{2}) d θ

Apply u-substitution

: \int_{0}^{\frac{π}{2}} cos (u) \frac{2}{π} d u

= \int_{0}^{\frac{π}{2}} cos (u) \frac{2}{π} d u

Take the constant out:

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

= \frac{2}{π} \cdot \int_{0}^{\frac{π}{2}} cos (u) d u

Use the common integral:

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

= \frac{2}{π} [sin (u)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= \frac{2}{π} \cdot 1

Simplify

= \frac{2}{π}

\int_{1}^{1} tan (x) d x

\int_{2}^{3} (e^{2 x} + e^{x}) d x

\int_{0}^{π} x cos (\frac{nπ x}{π}) d x

\int_{0}^{3} \frac{1}{x ^{4} + 1} d x

\int_{0}^{\frac{1}{2} π} cos (d) x d x

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