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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 Notation

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}

Popular Examples

integral from-pi to pi of sin(x)sin(2x)

\int_{- π}^{π} sin (x) sin (2 x) d x

integral from 5 to 5 of 4x

\int_{5}^{5} 4 x d x

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

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

integral from 0 to t of cos(t)

\int_{0}^{t} cos (t) d t

integral from 0 to pi of sin^4(θ)

\int_{0}^{π} sin^{4} (θ) d θ

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