What is the integral from a to b of 2x^2 ?

The integral from a to b of 2x^2 is (2(b^3-a^3))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from a to b of 2x^2

\int_{a}^{b} 2 x^{2} d x

\frac{2 ( b ^{3} - a ^{3} )}{3}

Solution steps

\int_{a}^{b} 2 x^{2} d x

Take the constant out:

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

= 2 \cdot \int_{a}^{b} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{a}^{b}

= 2 [\frac{x ^{3}}{3}]_{a}^{b}

Compute the boundaries:

\frac{b ^{3}}{3} - \frac{a ^{3}}{3}

= 2 (\frac{b ^{3}}{3} - \frac{a ^{3}}{3})

Simplify

= \frac{2 ( b ^{3} - a ^{3} )}{3}

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

\int_{12}^{16} (x^{2} - 6)^{\frac{1}{2}} d x

\int_{0}^{2 π} 4 d θ

\int_{\frac{x}{2}}^{1 - \frac{x}{2}} 2 - x - 2 y d y

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

What is the integral from a to b of 2x^2 ?
The integral from a to b of 2x^2 is (2(b^3-a^3))/3