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Popular >

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

Solution

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

Solution

2

Solution steps

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

Eliminate Absolutes

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

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

\int_{1}^{2} - 1 + x^{2} d x = \frac{4}{3}

= \frac{2}{3} + \frac{4}{3}

Simplify

\frac{2}{3} + \frac{4}{3} : 2

= 2

Graph

Popular Examples

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\int_{0}^{1} 10 x e^{x} d x

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\int_{- \frac{π}{2}}^{\frac{π}{2}} 4 cos^{2} (x) d x

integral from 0 to sin(x) of ln(t^3+1)

\int_{0}^{s i n (x)} ln (t^{3} + 1) d t

integral from 2 to infinity of xe^{-x/2}

\int_{2}^{\infty} x e^{- \frac{x}{2}} 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