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Popular >

integral from 0 to 2 of 1-x^2

Solution

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

Solution

- \frac{2}{3}

+1

Solution steps

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

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

= 2 - \frac{8}{3}

Simplify

2 - \frac{8}{3} : - \frac{2}{3}

= - \frac{2}{3}

Popular Examples

integral from 0 to 5/8 of 1/(64x^2+25)

\int_{0}^{\frac{5}{8}} \frac{1}{64 x ^{2} + 25} d x

integral from 1 to 4 of (x+1/x)^2

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

integral from 0 to infinity of cos(3x)

\int_{0}^{\infty} cos (3 x) d x

integral from 0 to 1 of xsqrt(1-1/4 x^2)

\int_{0}^{1} x 1 - \frac{1}{4} x^{2} d x

integral from 1 to 5 of (6x^2+7x)

\int_{1}^{5} (6 x^{2} + 7 x) d x

Frequently Asked Questions (FAQ)

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