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

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

Popular >

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

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

Apply u-substitution

: \int_{0}^{1} \frac{e ^{u} u}{2} d u

= \int_{0}^{1} \frac{e ^{u} u}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{1} e^{u} u d u

Apply Integration By Parts

: [e^{u} u - \int e^{u} d u]_{0}^{1}

= \frac{1}{2} [e^{u} u - \int e^{u} d u]_{0}^{1}

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

= \frac{1}{2} [e^{u} u - e^{u}]_{0}^{1}

Compute the boundaries:

1

= \frac{1}{2} \cdot 1

Simplify

= \frac{1}{2}

\int_{3}^{5} 5 d x

\int_{5}^{8} (\frac{5}{x ^{2}} - 1) d x

\int_{1}^{\infty} x \frac{3}{x ^{4}} d x

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

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

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