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

The integral from-1 to 3 of (2x^2-x+3)^2 is 3728/15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 3 of (2x^2-x+3)^2

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

\frac{3728}{15}

Decimal

248.53333 \dots

Solution steps

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

Expand

(2 x^{2} - x + 3)^{2} : 4 x^{4} - 4 x^{3} + 13 x^{2} - 6 x + 9

= \int_{- 1}^{3} 4 x^{4} - 4 x^{3} + 13 x^{2} - 6 x + 9 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_{- 1}^{3} 4 x^{4} d x - \int_{- 1}^{3} 4 x^{3} d x + \int_{- 1}^{3} 13 x^{2} d x - \int_{- 1}^{3} 6 x d x + \int_{- 1}^{3} 9 d x

\int_{- 1}^{3} 4 x^{4} d x = \frac{976}{5}

\int_{- 1}^{3} 4 x^{3} d x = 80

\int_{- 1}^{3} 13 x^{2} d x = \frac{364}{3}

\int_{- 1}^{3} 6 x d x = 24

\int_{- 1}^{3} 9 d x = 36

= \frac{976}{5} - 80 + \frac{364}{3} - 24 + 36

Simplify

\frac{976}{5} - 80 + \frac{364}{3} - 24 + 36 : \frac{3728}{15}

= \frac{3728}{15}

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

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

\int_{\frac{- π}{4}}^{\frac{π}{4}} tan (x) d x

\int_{2.5}^{3} (- x^{2} + 4) d x

\int_{0}^{\frac{π}{4}} sin^{3} (4 x) d x

What is the integral from-1 to 3 of (2x^2-x+3)^2 ?
The integral from-1 to 3 of (2x^2-x+3)^2 is 3728/15