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Popular >

integral of 4x-x^2

Solution

\int 4 x - x^{2} d x

Solution

2 x^{2} - \frac{x ^{3}}{3} + C

Solution steps

\int 4 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 4 x d x - \int x^{2} d x

\int 4 x d x = 2 x^{2}

\int x^{2} d x = \frac{x ^{3}}{3}

= 2 x^{2} - \frac{x ^{3}}{3}

Add a constant to the solution

= 2 x^{2} - \frac{x ^{3}}{3} + C

Popular Examples

sum from n=0 to infinity of ne^n

n = 0 \sum \infty n e^{n}

integral of x+10

\int x + 10 d x

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

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

(\partial)/(\partial x)((x^2)/(y^3))

\frac{\partial}{\partial x} (\frac{x ^{2}}{y ^{3}})

area x^2-1, 1/2 x^2 area

x^{2} - 1, \frac{1}{2} x^{2}

Frequently Asked Questions (FAQ)

What is the integral of 4x-x^2 ?
The integral of 4x-x^2 is 2x^2-(x^3)/3+C