en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

52

Solution steps

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

Expand

(3 x + 1)^{2} : 9 x^{2} + 6 x + 1

= \int_{- 2}^{2} 9 x^{2} + 6 x + 1 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}^{2} 9 x^{2} d x + \int_{- 2}^{2} 6 x d x + \int_{- 2}^{2} 1 d x

\int_{- 2}^{2} 9 x^{2} d x = 48

\int_{- 2}^{2} 6 x d x = 0

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

= 48 + 0 + 4

Simplify

= 52

Popular Examples

integral from 0 to 1 of ax^2+bx^3

\int_{0}^{1} a x^{2} + b x^{3} d x

integral from 0 to (2pi)/ω of tsin(ω)t

\int_{0}^{\frac{2 π}{ω}} t sin (ω) t d t

integral from 2pi to 0 of tan(x)

\int_{2 π}^{0} tan (x) d x

integral from 0 to pi of cos^2(3x)

\int_{0}^{π} cos^{2} (3 x) d x

integral from 0 to 4 of e^{x^2}

\int_{0}^{4} e^{x^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral from-2 to 2 of (3x+1)^2 ?
The integral from-2 to 2 of (3x+1)^2 is 52