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

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

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

\int_{0}^{π} x cos (x^{2}) d x

\frac{1}{2} sin (π^{2})

Decimal

- 0.2151506085

Solution steps

\int_{0}^{π} x cos (x^{2}) d x

Apply u-substitution

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

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{0}^{π^{2}}

Compute the boundaries:

sin (π^{2})

= \frac{1}{2} sin (π^{2})

y^{^{'}} = (2 y + 22)^{0.5}

d er i v a t i v e f (x) = (x^{3} + 1) \cdot 3 x^{2}

l a pl a ce t r an s f or m t sin (9 t)

a re a y = x^{2} - x, y = 0

in v erse l a pl a ce \frac{2 s + 9}{s ^{2} + 4 s + 40}

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