What is the integral from 0 to 1 of x^4cos(x^5) ?

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

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integral from 0 to 1 of x^4cos(x^5)

\int_{0}^{1} x^{4} cos (x^{5}) d x

\frac{1}{5} sin (1)

Decimal

0.16829 \dots

Solution steps

\int_{0}^{1} x^{4} cos (x^{5}) d x

Apply u-substitution

: \int_{0}^{1} \frac{cos ( u )}{5} d u

= \int_{0}^{1} \frac{cos ( u )}{5} d u

Take the constant out:

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

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

Use the common integral:

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

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

Compute the boundaries:

sin (1)

= \frac{1}{5} sin (1)

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\int_{0}^{3} (8 x - 1)^{2} d x

\int_{0}^{1} y 4 y^{2} + 1 d y

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