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Popular Calculus >

integral from-2 to 2 of 4-y^2

Solution

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

Solution

\frac{32}{3}

+1

Decimal

10.66666 \dots

Solution steps

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

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

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

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

= 16 - \frac{16}{3}

Simplify

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

= \frac{32}{3}

Graph

Popular Examples

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

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

integral from-1 to 1 of 1/(5-4x)

\int_{- 1}^{1} \frac{1}{5 - 4 x} d x

integral from 2 to 4 of 2

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

integral from 1 to 2 of (1+1/u+1/(u^2))

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

integral from 2 to 3 of x^4

\int_{2}^{3} x^{4} d x

Frequently Asked Questions (FAQ)

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