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Popular >

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

Solution

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

Solution

\frac{32}{3}

+1

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}

Popular Examples

integral from 1 to 3 of x/((x^2+7)^3)

\int_{1}^{3} \frac{x}{( x ^{2} + 7 ) ^{3}} d x

integral from 5 to 6 of 2^{-x}

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

integral from 0 to 2 of (e^{3y}-3)/(e^{3y)-9y+18}

\int_{0}^{2} \frac{e ^{3 y} - 3}{e ^{3 y} - 9 y + 18} d y

integral from 0 to 1 of x^2sqrt(1+x^3)

\int_{0}^{1} x^{2} 1 + x^{3} d x

integral from x to 2x of t^3

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

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