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Popular >

integral from 0 to 1 of 2y^2-2y

Solution

\int_{0}^{1} 2 y^{2} - 2 y d y

Solution

- \frac{1}{3}

+1

Decimal Notation

- 0.33333 \dots

Solution steps

\int_{0}^{1} 2 y^{2} - 2 y 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}^{1} 2 y^{2} d y - \int_{0}^{1} 2 y d y

\int_{0}^{1} 2 y^{2} d y = \frac{2}{3}

\int_{0}^{1} 2 y d y = 1

= \frac{2}{3} - 1

Simplify

\frac{2}{3} - 1 : - \frac{1}{3}

= - \frac{1}{3}

Popular Examples

integral from-8 to 3 of sqrt(1+|x|)

\int_{- 8}^{3} 1 + ∣ x ∣ d x

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

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

integral from 0 to 2pi of 1/(1+sin^2(x))

\int_{0}^{2 π} \frac{1}{1 + sin ^{2} ( x )} d x

integral from a to b of ln(r^2)r

\int_{a}^{b} ln (r^{2}) r d r

integral from 0 to 8 of 2sqrt(x)+3

\int_{0}^{8} 2 x + 3 d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of 2y^2-2y ?
The integral from 0 to 1 of 2y^2-2y is -1/3