What is the integral from 2 to 5 of (x^3-x^2+8) ?

The integral from 2 to 5 of (x^3-x^2+8) is 549/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 5 of (x^3-x^2+8)

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

\frac{549}{4}

Decimal

137.25

Solution steps

\int_{2}^{5} x^{3} - x^{2} + 8 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_{2}^{5} x^{3} d x - \int_{2}^{5} x^{2} d x + \int_{2}^{5} 8 d x

\int_{2}^{5} x^{3} d x = \frac{609}{4}

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} 8 d x = 24

= \frac{609}{4} - 39 + 24

Simplify

\frac{609}{4} - 39 + 24 : \frac{549}{4}

= \frac{549}{4}

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

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

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

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

\int_{- 6}^{6} x^{2} - 25 d x

What is the integral from 2 to 5 of (x^3-x^2+8) ?
The integral from 2 to 5 of (x^3-x^2+8) is 549/4