What is the integral from 0 to 2 of-4x^2+8x^3 ?

The integral from 0 to 2 of-4x^2+8x^3 is 64/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of-4x^2+8x^3

\int_{0}^{2} - 4 x^{2} + 8 x^{3} d x

\frac{64}{3}

Decimal

21.33333 \dots

Solution steps

\int_{0}^{2} - 4 x^{2} + 8 x^{3} 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}^{2} 4 x^{2} d x + \int_{0}^{2} 8 x^{3} d x

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

\int_{0}^{2} 8 x^{3} d x = 32

= - \frac{32}{3} + 32

Simplify

- \frac{32}{3} + 32 : \frac{64}{3}

= \frac{64}{3}

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

\int_{1}^{2} 2^{5 x} d x

\int_{1}^{\infty} 2 x^{- 2} d x

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

\int_{0}^{1} 25 - (t - 5)^{2} d t

What is the integral from 0 to 2 of-4x^2+8x^3 ?
The integral from 0 to 2 of-4x^2+8x^3 is 64/3