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Popular >

integral from 0 to 2 of 4y-2y^2

Solution

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

Solution

\frac{8}{3}

+1

Decimal Notation

2.66666 \dots

Solution steps

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

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

\int_{0}^{2} 2 y^{2} d y = \frac{16}{3}

= 8 - \frac{16}{3}

Simplify

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

= \frac{8}{3}

Popular Examples

integral from 0 to pi of xycos(y)

\int_{0}^{π} x y cos (y) d y

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\int_{1}^{4} x^{3} - 1 d x

integral from 4 to 2 of 6x

\int_{4}^{2} 6 x d x

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

\int_{- 1}^{1} x cos (x^{2}) d x

integral from 0 to x of 30e^{-30x}

\int_{0}^{x} 30 e^{- 30 x} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of 4y-2y^2 ?
The integral from 0 to 2 of 4y-2y^2 is 8/3