What is the integral from 0 to 1 of e^{x^3}x^2 ?

The integral from 0 to 1 of e^{x^3}x^2 is (e-1)/3

Popular >

integral from 0 to 1 of e^{x^3}x^2

\int_{0}^{1} e^{x^{3}} x^{2} d x

\frac{e - 1}{3}

Decimal

0.57276 \dots

Solution steps

\int_{0}^{1} e^{x^{3}} x^{2} d x

Apply u-substitution

: \int_{0}^{1} \frac{e ^{u}}{3} d u

= \int_{0}^{1} \frac{e ^{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}^{1} e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{3} [e^{u}]_{0}^{1}

Compute the boundaries:

e - 1

= \frac{1}{3} (e - 1)

Simplify

= \frac{e - 1}{3}

\int_{- 1}^{5} 2 x + 4 d x

\int_{0}^{1} x^{2} + x - 2 d x

\int_{0}^{x} \frac{t}{2} d t

\int_{0}^{2} (t i + e^{t} j - t e^{t} k) d t

\int_{x^{3}}^{x} x^{2} + 3 y^{2} d y

What is the integral from 0 to 1 of e^{x^3}x^2 ?
The integral from 0 to 1 of e^{x^3}x^2 is (e-1)/3