What is the integral from 0 to pi/2 of cos(x/2) ?

The integral from 0 to pi/2 of cos(x/2) is square root of 2

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integral from 0 to pi/2 of cos(x/2)

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

2

Decimal

1.41421 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{\frac{π}{4}} cos (u) \cdot 2 d u

= \int_{0}^{\frac{π}{4}} cos (u) \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int_{0}^{\frac{π}{4}} cos (u) d u

Use the common integral:

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

= 2 [sin (u)]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{1}{2}

= 2 \cdot \frac{1}{2}

Simplify

= 2

\frac{d}{d x} (\frac{6 e ^{x}}{7 x})

\frac{d P}{d t} = 5 Pt

\frac{d}{d x} ((3 x + 1) (2 x + 6))

y = x^{3} - 5 x, (- 1, 5)

\int x^{3} e^{x^{2} + 1} d x

What is the integral from 0 to pi/2 of cos(x/2) ?
The integral from 0 to pi/2 of cos(x/2) is square root of 2