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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Apply u-substitution

: \int_{0}^{1} \frac{e ^{u^{\frac{2}{3}}} u ^{\frac{1}{3}}}{3} d u

= \int_{0}^{1} \frac{e ^{u^{\frac{2}{3}}} u ^{\frac{1}{3}}}{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^{\frac{2}{3}}} u^{\frac{1}{3}} d u

Apply u-substitution

: \int_{0}^{1} \frac{3 e ^{v} v}{2} d v

= \frac{1}{3} \cdot \int_{0}^{1} \frac{3 e ^{v} v}{2} d v

Take the constant out:

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

= \frac{1}{3} \cdot \frac{3}{2} \cdot \int_{0}^{1} e^{v} v d v

Apply Integration By Parts

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

= \frac{1}{3} \cdot \frac{3}{2} [e^{v} v - \int e^{v} d v]_{0}^{1}

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

= \frac{1}{3} \cdot \frac{3}{2} [e^{v} v - e^{v}]_{0}^{1}

Simplify

\frac{1}{3} \cdot \frac{3}{2} [e^{v} v - e^{v}]_{0}^{1} : \frac{1}{2} [e^{v} v - e^{v}]_{0}^{1}

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

Compute the boundaries:

1

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

Simplify

= \frac{1}{2}

\int arctan (x y) d x

y = \frac{5}{x}, y = \frac{10}{x ^{2}}, x = 6

\int \frac{y ^{2}}{y ^{3} + 1} d y

\int \frac{( e ^{x} )}{2} d x

x \to \frac{1}{2} lim (\frac{x ^{2}}{2})

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