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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

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

2y^{''}-6y^'+y=0

2 y^{^{''}} - 6 y^{^{'}} + y = 0

integral of 5sec^2(x)

\int 5 sec^{2} (x) d x

6x^2y^'=y^'+6xe^{-y}

6 x^{2} y^{^{'}} = y^{^{'}} + 6 x e^{- y}

integral of (2x+1)/(x^2+2x+10)

\int \frac{2 x + 1}{x ^{2} + 2 x + 10} d x

limit as x approaches 2 of x^2-3x+1

x \to 2 lim (x^{2} - 3 x + 1)

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