What is the integral from-7 to 7 of (49-x^2) ?

The integral from-7 to 7 of (49-x^2) is 1372/3

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integral from-7 to 7 of (49-x^2)

\int_{- 7}^{7} (49 - x^{2}) d x

\frac{1372}{3}

Decimal

457.33333 \dots

Solution steps

\int_{- 7}^{7} 49 - 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_{- 7}^{7} 49 d x - \int_{- 7}^{7} x^{2} d x

\int_{- 7}^{7} 49 d x = 686

\int_{- 7}^{7} x^{2} d x = \frac{686}{3}

= 686 - \frac{686}{3}

Simplify

686 - \frac{686}{3} : \frac{1372}{3}

= \frac{1372}{3}

\frac{d}{d x} (ln (\frac{x + 3}{e ^{3 x}}))

\frac{\partial}{\partial x} (\frac{x}{9 + y})

d er i v a t i v e y = 7 x^{3} - 6 x^{2} - \frac{8}{x}

4 y^{^{''}} - y^{^{'}} + y = 0

y^{^{''}} + 2 y^{^{'}} - y = 10

What is the integral from-7 to 7 of (49-x^2) ?
The integral from-7 to 7 of (49-x^2) is 1372/3