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Popular >

integral from-1 to 1 of (1-y^2)

Solution

\int_{- 1}^{1} (1 - y^{2}) d y

Solution

\frac{4}{3}

+1

Decimal

1.33333 \dots

Solution steps

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

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

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

= 2 - \frac{2}{3}

Simplify

2 - \frac{2}{3} : \frac{4}{3}

= \frac{4}{3}

Graph

Popular Examples

integral from 0 to 1 of x^2+2x-1

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

integral from 0 to 1 of x^6+x^8

\int_{0}^{1} x^{6} + x^{8} d x

integral from 0 to 6 of x^2+3

\int_{0}^{6} x^{2} + 3 d x

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

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

integral from 4 to x of 1/(1+x^3)

\int_{4}^{x} \frac{1}{1 + x ^{3}} d x

Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of (1-y^2) ?
The integral from-1 to 1 of (1-y^2) is 4/3