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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 1 of 3x^2sin(x^3)

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

- cos (1) + 1

Decimal

0.45969 \dots

Solution steps

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

Take the constant out:

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

= 3 \cdot \int_{0}^{1} x^{2} sin (x^{3}) d x

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= 3 \cdot \frac{1}{3} [- cos (u)]_{0}^{1}

Simplify

3 \cdot \frac{1}{3} [- cos (u)]_{0}^{1} : [- cos (u)]_{0}^{1}

= [- cos (u)]_{0}^{1}

Compute the boundaries:

- cos (1) + 1

= - cos (1) + 1

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