en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral from 4 to-4 of (3r+2)^2

Solution

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

Solution

- 416

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 4}^{4} (3 r + 2)^{2} d r

Expand

(3 r + 2)^{2} : 9 r^{2} + 12 r + 4

= - \int_{- 4}^{4} 9 r^{2} + 12 r + 4 d r

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - (\int_{- 4}^{4} 9 r^{2} d r + \int_{- 4}^{4} 12 r d r + \int_{- 4}^{4} 4 d r)

\int_{- 4}^{4} 9 r^{2} d r = 384

\int_{- 4}^{4} 12 r d r = 0

\int_{- 4}^{4} 4 d r = 32

= - (384 + 0 + 32)

Simplify

= - 416

Graph

Popular Examples

integral from-6 to 4 of sqrt(24-2x-x^2)

integral from 0 to t of (y(u)-1)

integral from 0 to 2 of 12x^3sqrt(x^4+9)

integral from 0 to 2 of 2cos((npix)/2)

integral from 1 to 4 of 8x

Frequently Asked Questions (FAQ)

What is the integral from 4 to-4 of (3r+2)^2 ?
The integral from 4 to-4 of (3r+2)^2 is -416