What is the integral from 0 to 1 of (-3x^2+4x+3) ?

The integral from 0 to 1 of (-3x^2+4x+3) is 4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of (-3x^2+4x+3)

\int_{0}^{1} (- 3 x^{2} + 4 x + 3) d x

4

Solution steps

\int_{0}^{1} - 3 x^{2} + 4 x + 3 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_{0}^{1} 3 x^{2} d x + \int_{0}^{1} 4 x d x + \int_{0}^{1} 3 d x

\int_{0}^{1} 3 x^{2} d x = 1

\int_{0}^{1} 4 x d x = 2

\int_{0}^{1} 3 d x = 3

= - 1 + 2 + 3

Simplify

= 4

\int_{0}^{1} \frac{1}{1 + 2 x - 1} d x

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

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

\int_{- 1}^{2} 8 - x^{2} - x d x

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

What is the integral from 0 to 1 of (-3x^2+4x+3) ?
The integral from 0 to 1 of (-3x^2+4x+3) is 4