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Popular Calculus >

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

Solution

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

Solution

\frac{2}{3}

+1

Decimal

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}

Graph

Popular Examples

integral from-3 to 3 of ln(x+4)

\int_{- 3}^{3} ln (x + 4) d x

integral from x to 3x-x^2 of x^2-xy

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

integral from 2 to 3 of (3x-2)/(x^3-x^2)

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

integral from-2 to 2 of xsin((npix)/2)

\int_{- 2}^{2} x sin (\frac{nπ x}{2}) d x

integral from 4 to 10 of 1/(x-2)

\int_{4}^{10} \frac{1}{x - 2} d x

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