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Popular >

integral of 4r

Solution

\int 4 r d r

Solution

2 r^{2} + C

Solution steps

\int 4 r d r

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int r d r

Apply the Power Rule

: \frac{r ^{2}}{2}

= 4 \cdot \frac{r ^{2}}{2}

Simplify

4 \cdot \frac{r ^{2}}{2} : 2 r^{2}

= 2 r^{2}

Add a constant to the solution

= 2 r^{2} + C

Popular Examples

integral of 1/(x-9)

\int \frac{1}{x - 9} d x

implicit y/(x-5y)=x^7+9 implicit derivative

\frac{y}{x - 5 y} = x^{7} + 9

xe^y(dy)/(dx)=2(e^y+x^3e^{2x})

x e^{y} \frac{d y}{d x} = 2 (e^{y} + x^{3} e^{2 x})

(dy)/(dx)=e^{5x}+10y

\frac{d y}{d x} = e^{5 x} + 10 y

integral from 0 to 1 of (1+e^x)/(e^x)

\int_{0}^{1} \frac{1 + e ^{x}}{e ^{x}} d x

Frequently Asked Questions (FAQ)

What is the integral of 4r ?
The integral of 4r is 2r^2+C