What is the integral from 0 to 2 of x^2cos(x^3) ?

The integral from 0 to 2 of x^2cos(x^3) is 1/3 sin(8)

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integral from 0 to 2 of x^2cos(x^3)

\int_{0}^{2} x^{2} cos (x^{3}) d x

\frac{1}{3} sin (8)

Decimal

0.32978 \dots

Solution steps

\int_{0}^{2} x^{2} cos (x^{3}) d x

Apply u-substitution

= \int_{0}^{8} \frac{cos ( u )}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{0}^{8} cos (u) d u

Use the common integral:

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

= \frac{1}{3} [sin (u)]_{0}^{8}

Compute the boundaries:

sin (8)

= \frac{1}{3} sin (8)

What is the integral from 0 to 2 of x^2cos(x^3) ?
The integral from 0 to 2 of x^2cos(x^3) is 1/3 sin(8)