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

The integral from 0 to pi/2 of xcos(x^2) is 1/2 sin((pi^2)/4)

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integral from 0 to pi/2 of xcos(x^2)

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

\frac{1}{2} sin (\frac{π ^{2}}{4})

Decimal

0.31213 \dots

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{π ^{2}}{4}} cos (u) d u

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{0}^{\frac{π ^{2}}{4}}

Compute the boundaries:

sin (\frac{π ^{2}}{4})

= \frac{1}{2} sin (\frac{π ^{2}}{4})

(5 - 5 x^{3})^{3} + \frac{1}{5 - 5 x ^{3}}

\int xx d x

\frac{d}{d x} (\frac{2}{x - 6})

\frac{d}{d x} (6 x - 2)

arcsin (\frac{6}{7} x)

What is the integral from 0 to pi/2 of xcos(x^2) ?
The integral from 0 to pi/2 of xcos(x^2) is 1/2 sin((pi^2)/4)