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

The integral from 0 to 1 of (x^3+3x^2) is 5/4

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^3+3x^2)

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

\frac{5}{4}

Decimal Notation

1.25

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} x^{3} d x + \int_{0}^{1} 3 x^{2} d x

\int_{0}^{1} x^{3} d x = \frac{1}{4}

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

= \frac{1}{4} + 1

Simplify

\frac{1}{4} + 1 : \frac{5}{4}

= \frac{5}{4}

\int_{0}^{3} \frac{3 x ( 8 - x )}{256} d x

\int_{1}^{\infty} \frac{1}{2 x + 3} d x

\int_{0}^{\frac{π}{2}} \frac{1}{3 + cos ( 2 a )} d a

\int_{- 1}^{3} (- 3 x^{2} + 8 x + 5) d x

\int_{- 1}^{1} 8^{x} d x

What is the integral from 0 to 1 of (x^3+3x^2) ?
The integral from 0 to 1 of (x^3+3x^2) is 5/4