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Popular Calculus >

integral from-2 to 2 of (6-x^2)

Solution

\int_{- 2}^{2} (6 - x^{2}) d x

Solution

\frac{56}{3}

+1

Decimal

18.66666 \dots

Solution steps

\int_{- 2}^{2} 6 - 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_{- 2}^{2} 6 d x - \int_{- 2}^{2} x^{2} d x

\int_{- 2}^{2} 6 d x = 24

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

= 24 - \frac{16}{3}

Simplify

24 - \frac{16}{3} : \frac{56}{3}

= \frac{56}{3}

Graph

Popular Examples

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\int_{1}^{x} \frac{1}{t ^{2}} d t

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\int_{4}^{8} (x - 4) d x

integral from 0 to y of e^{x+y}

\int_{0}^{y} e^{x + y} d x

integral from-2 to 2 of (8-|x|)

\int_{- 2}^{2} (8 - ∣ x ∣) d x

integral from-2 to 0 of e^x

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

Frequently Asked Questions (FAQ)

What is the integral from-2 to 2 of (6-x^2) ?
The integral from-2 to 2 of (6-x^2) is 56/3