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Popular Calculus >

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

Solution

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

Solution

\frac{2}{3}

+1

Decimal

0.66666 \dots

Solution steps

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

Eliminate Absolutes

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

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

\int_{- 1}^{0} 1 d x = 1

= - \frac{1}{3} + 1

Simplify

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

= \frac{2}{3}

Graph

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sqrt(x)+sqrt(y)y^'=0,y(1)=9

Frequently Asked Questions (FAQ)

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