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Popular >

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

Solution

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

Solution

\frac{16}{3}

+1

Decimal

5.33333 \dots

Solution steps

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

\int_{0}^{2} 4 x d x = 8

\int_{0}^{2} x^{2} d x = \frac{8}{3}

= 8 - \frac{8}{3}

Simplify

8 - \frac{8}{3} : \frac{16}{3}

= \frac{16}{3}

Graph

Popular Examples

integral from 0 to x of (t^2+1)

\int_{0}^{x} (t^{2} + 1) d t

integral from 1 to 2 of (2^x)/(x^2)

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

integral from-1 to 1 of 1/(x-2)

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

integral from 1 to 2 of 4x^3+3x^2+4x+2

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

integral from 0 to 2pi of x*sin(nx)

\int_{0}^{2 π} x \cdot sin (n x) d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of (4x-x^2) ?
The integral from 0 to 2 of (4x-x^2) is 16/3