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Popular >

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

Solution

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

Solution

\frac{32}{3}

+1

Decimal Notation

10.66666 \dots

Solution steps

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

Eliminate Absolutes

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

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

\int_{- 2}^{2} 4 d x = 16

= - \frac{16}{3} + 16

Simplify

- \frac{16}{3} + 16 : \frac{32}{3}

= \frac{32}{3}

Popular Examples

integral from 1 to 2 of e^yy-e^y

\int_{1}^{2} e^{y} y - e^{y} d y

integral from-pi/4 to pi/4 of sin(t)

\int_{- \frac{π}{4}}^{\frac{π}{4}} sin (t) d t

integral from-5 to 5 of x^{10}sin(x)

\int_{- 5}^{5} x^{10} sin (x) d x

integral from 0 to 3 of 5x^2+9x

\int_{0}^{3} 5 x^{2} + 9 x d x

integral from 1 to 3 of (t^6)/(1+t^4)

\int_{1}^{3} \frac{t ^{6}}{1 + t ^{4}} d t

Frequently Asked Questions (FAQ)

What is the integral from-2 to 2 of |x^2-4| ?
The integral from-2 to 2 of |x^2-4| is 32/3