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Popular >

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

Solution

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

Solution

\frac{4}{3}

+1

Decimal

1.33333 \dots

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

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

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

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

= - (\frac{2}{3} - 2)

Simplify

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

= \frac{4}{3}

Graph

Popular Examples

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

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

integral from 0 to 3 of e^{t^2}

\int_{0}^{3} e^{t^{2}} d t

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

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

integral from 0 to 9 of 3-sqrt(x)

\int_{0}^{9} 3 - x d x

integral from 1 to 4 of (x/2-4/x)

\int_{1}^{4} (\frac{x}{2} - \frac{4}{x}) d x

Frequently Asked Questions (FAQ)

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