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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

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 0 to 2 of x^3-x^2-2x

\int_{0}^{2} x^{3} - x^{2} - 2 x d x

integral from 0 to 1 of sqrt(y)

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

integral from 1 to 5 of-x^2+6x-5

\int_{1}^{5} - x^{2} + 6 x - 5 d x

integral from 0 to 1 of e^{2x+3}

\int_{0}^{1} e^{2 x + 3} d x

integral from 0 to ln(5) of 2e^{3x}

\int_{0}^{l n (5)} 2 e^{3 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