What is the integral from-7 to 7 of 1/2 (49-x^2) ?

The integral from-7 to 7 of 1/2 (49-x^2) is 686/3

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integral from-7 to 7 of 1/2 (49-x^2)

\int_{- 7}^{7} \frac{1}{2} (49 - x^{2}) d x

\frac{686}{3}

Decimal Notation

228.66666 \dots

Solution steps

\int_{- 7}^{7} \frac{1}{2} (49 - x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \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

= \frac{1}{2} (\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}

= \frac{1}{2} (686 - \frac{686}{3})

Simplify

\frac{1}{2} (686 - \frac{686}{3}) : \frac{686}{3}

= \frac{686}{3}

t \to π lim (sin (\frac{t}{2}))

\frac{10}{s \cdot ( s + 1 ) \cdot ( s + 10 )}

2 t

\frac{\partial}{\partial x} (cos (2 x + 6 y))

What is the integral from-7 to 7 of 1/2 (49-x^2) ?
The integral from-7 to 7 of 1/2 (49-x^2) is 686/3