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Popular >

integral from 0 to 2 of (2y-y^2)

Solution

\int_{0}^{2} (2 y - y^{2}) d y

Solution

\frac{4}{3}

+1

Decimal Notation

1.33333 \dots

Solution steps

\int_{0}^{2} 2 y - y^{2} d y

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} 2 y d y - \int_{0}^{2} y^{2} d y

\int_{0}^{2} 2 y d y = 4

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

= 4 - \frac{8}{3}

Simplify

4 - \frac{8}{3} : \frac{4}{3}

= \frac{4}{3}

Popular Examples

integral from 0 to pi/3 of 9sec^2(x)

\int_{0}^{\frac{π}{3}} 9 sec^{2} (x) d x

integral from 0 to 1 of x^2sqrt(x^3+1)

\int_{0}^{1} x^{2} x^{3} + 1 d x

integral from 0 to 9 of 1/(x^2+81)

\int_{0}^{9} \frac{1}{x ^{2} + 81} d x

integral from 0 to ln(4) of 6e^{2x}

\int_{0}^{l n (4)} 6 e^{2 x} d x

integral from 0 to 4pi of sin(2x)

\int_{0}^{4 π} sin (2 x) d x

Frequently Asked Questions (FAQ)

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