en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral from 0 to 3 of (5x-x^2)

Solution

\int_{0}^{3} (5 x - x^{2}) d x

Solution

\frac{27}{2}

+1

Decimal

13.5

Solution steps

\int_{0}^{3} 5 x - x^{2} 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}^{3} 5 x d x - \int_{0}^{3} x^{2} d x

\int_{0}^{3} 5 x d x = \frac{45}{2}

\int_{0}^{3} x^{2} d x = 9

= \frac{45}{2} - 9

Simplify

\frac{45}{2} - 9 : \frac{27}{2}

= \frac{27}{2}

Graph

Popular Examples

y^{''}-4y^'+4y=t^{-7}e^{2t}

integral of 1/((1-y)(2-y))

laplacetransform f(s)=2te^{-5t}

area f(x)=x^2+2x,[1,2]

derivative of-2x^2+2x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of (5x-x^2) ?
The integral from 0 to 3 of (5x-x^2) is 27/2