What is the integral from-2 to 1 of pi(x^2+x-2)^2 ?

The integral from-2 to 1 of pi(x^2+x-2)^2 is pi 81/10

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-2 to 1 of pi(x^2+x-2)^2

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

π \frac{81}{10}

Solution steps

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

Take the constant out:

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

= π \cdot \int_{- 2}^{1} (x^{2} + x - 2)^{2} d x

Expand

(x^{2} + x - 2)^{2} : x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 4

= π \cdot \int_{- 2}^{1} x^{4} + 2 x^{3} - 3 x^{2} - 4 x + 4 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

= π (\int_{- 2}^{1} x^{4} d x + \int_{- 2}^{1} 2 x^{3} d x - \int_{- 2}^{1} 3 x^{2} d x - \int_{- 2}^{1} 4 x d x + \int_{- 2}^{1} 4 d x)

\int_{- 2}^{1} x^{4} d x = \frac{33}{5}

\int_{- 2}^{1} 2 x^{3} d x = - \frac{15}{2}

\int_{- 2}^{1} 3 x^{2} d x = 9

\int_{- 2}^{1} 4 x d x = - 6

\int_{- 2}^{1} 4 d x = 12

= π (\frac{33}{5} - \frac{15}{2} - 9 - (- 6) + 12)

Simplify

π (\frac{33}{5} - \frac{15}{2} - 9 - (- 6) + 12) : π \frac{81}{10}

= π \frac{81}{10}

\int_{0}^{5} 2 t d t

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

\int_{0}^{25} y + 11 d y

\int_{0}^{\infty} 18 e^{- 2 x} d x

\int_{0}^{25} sin (x) d x

What is the integral from-2 to 1 of pi(x^2+x-2)^2 ?
The integral from-2 to 1 of pi(x^2+x-2)^2 is pi 81/10