What is the integral from 0 to pi of x^4cos(2x^5) ?

The integral from 0 to pi of x^4cos(2x^5) is 1/10 sin(2pi^5)

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integral from 0 to pi of x^4cos(2x^5)

\int_{0}^{π} x^{4} cos (2 x^{5}) d x

\frac{1}{10} sin (2 π^{5})

Solution steps

\int_{0}^{π} x^{4} cos (2 x^{5}) d x

Apply u-substitution

: \int_{0}^{2 π^{5}} \frac{cos ( u )}{10} d u

= \int_{0}^{2 π^{5}} \frac{cos ( u )}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int_{0}^{2 π^{5}} cos (u) d u

Use the common integral:

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

= \frac{1}{10} [sin (u)]_{0}^{2 π^{5}}

Compute the boundaries:

sin (2 π^{5})

= \frac{1}{10} sin (2 π^{5})

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What is the integral from 0 to pi of x^4cos(2x^5) ?
The integral from 0 to pi of x^4cos(2x^5) is 1/10 sin(2pi^5)