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

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

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integral from 0 to 1 of cos((pix)/2)

\int_{0}^{1} cos (\frac{π x}{2}) d x

\frac{2}{π}

Decimal

0.63661 \dots

Solution steps

\int_{0}^{1} cos (\frac{π x}{2}) d x

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}

y^{^{''}} + 4 y^{^{'}} = (4 t - 4) sin (3 t)

n = 0 \sum \infty 0. 8^{n}

e^{x} (x + x x)

\frac{d}{d x} (ln (\frac{5 x ^{2} + x + 6}{x ^{3}}))

\int_{0}^{1} 12 e^{3 x} d x

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