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Popular >

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

Solution

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

Solution

- \frac{2}{3}

+1

Decimal Notation

- 0.66666 \dots

Solution steps

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

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

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

= \frac{1}{3} - 1

Simplify

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

= - \frac{2}{3}

Popular Examples

integral from 0 to pi/3 of 5sec^2(x)

\int_{0}^{\frac{π}{3}} 5 sec^{2} (x) d x

integral from-3 to 3 of x^{1/3}

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

integral from 0 to 2 of (y^2)/(y^3+1)

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

integral from-1 to 1 of arctan(x)

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

integral from 0 to 2pi of-4sin^2(t)

\int_{0}^{2 π} - 4 sin^{2} (t) d t

Frequently Asked Questions (FAQ)

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