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

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

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

\int_{0}^{π} x cos (2 x^{2}) d x

\frac{1}{4} sin (2 π^{2})

Decimal Notation

0.19421 \dots

Solution steps

\int_{0}^{π} x cos (2 x^{2}) d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{4} [sin (u)]_{0}^{2 π^{2}}

Compute the boundaries:

sin (2 π^{2})

= \frac{1}{4} sin (2 π^{2})

\int_{1}^{3} - x^{2} + x d x

\int_{0}^{π} cos (x) x d x

\int_{π}^{0} cos (x) d x

\int_{1}^{8} 4 x^{\frac{1}{3}} d x

\int_{2}^{4} x^{2} - 3 x + 4 d x

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