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Popular >

integral from 0 to 1 of |x^2-4|

Solution

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

Solution

\frac{11}{3}

+1

Decimal

3.66666 \dots

Solution steps

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

Eliminate Absolutes

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

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

\int_{0}^{1} 4 d x = 4

= - \frac{1}{3} + 4

Simplify

- \frac{1}{3} + 4 : \frac{11}{3}

= \frac{11}{3}

Graph

Popular Examples

integral from 0 to pi of 2xsin(nx)

\int_{0}^{π} 2 x sin (n x) d x

integral from 5 to 6 of x^2+2x-16

\int_{5}^{6} x^{2} + 2 x - 16 d x

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

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

integral from 0 to pi of |cos(x+y)|

\int_{0}^{π} ∣ cos (x + y) ∣ d x

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

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of |x^2-4| ?
The integral from 0 to 1 of |x^2-4| is 11/3