What is the integral from-8 to 8 of (64-x^2) ?

The integral from-8 to 8 of (64-x^2) is 2048/3

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integral from-8 to 8 of (64-x^2)

\int_{- 8}^{8} (64 - x^{2}) d x

\frac{2048}{3}

Decimal Notation

682.66666 \dots

Solution steps

\int_{- 8}^{8} 64 - 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_{- 8}^{8} 64 d x - \int_{- 8}^{8} x^{2} d x

\int_{- 8}^{8} 64 d x = 1024

\int_{- 8}^{8} x^{2} d x = \frac{1024}{3}

= 1024 - \frac{1024}{3}

Simplify

1024 - \frac{1024}{3} : \frac{2048}{3}

= \frac{2048}{3}

\frac{2}{( s + 3 )}

\frac{d}{d x} (\frac{1}{sin ( 3 x )})

\frac{d}{d x} (\frac{x ^{2} + 2 x - 6}{( x + 1 ) ^{2}})

(x^{2} + 1) y^{^{''}} - 2 x y^{^{'}} + 2 y = 0

f (x) = 6 e^{x} + x, (0, 6)

What is the integral from-8 to 8 of (64-x^2) ?
The integral from-8 to 8 of (64-x^2) is 2048/3