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Popular >

integral from 0 to 1 of 1-y^2

Solution

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

Solution

\frac{2}{3}

+1

Decimal Notation

0.66666 \dots

Solution steps

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

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

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

= 1 - \frac{1}{3}

Simplify

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

= \frac{2}{3}

Popular Examples

integral from 7 to 8 of (9/(x^2)-1)

\int_{7}^{8} (\frac{9}{x ^{2}} - 1) d x

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

\int_{0}^{1} (x^{3} - x^{2}) d x

integral from 1 to e of (4x+2/x)ln(x)

\int_{1}^{e} (4 x + \frac{2}{x}) ln (x) d x

integral from 2 to 3 of 3^{5x}

\int_{2}^{3} 3^{5 x} d x

integral from 2 to 3 of-t^2+2t+3

\int_{2}^{3} - t^{2} + 2 t + 3 d t

Frequently Asked Questions (FAQ)

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