What is the integral from-5 to 5 of (x-sqrt(25-x^2)) ?

The integral from-5 to 5 of (x-sqrt(25-x^2)) is -(25pi)/2

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integral from-5 to 5 of (x-sqrt(25-x^2))

\int_{- 5}^{5} (x - 25 - x^{2}) d x

- \frac{25 π}{2}

Decimal Notation

- 39.26990 \dots

Solution steps

\int_{- 5}^{5} x - 25 - 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_{- 5}^{5} x d x - \int_{- 5}^{5} 25 - x^{2} d x

\int_{- 5}^{5} x d x = 0

\int_{- 5}^{5} 25 - x^{2} d x = \frac{25 π}{2}

= 0 - \frac{25 π}{2}

Simplify

= - \frac{25 π}{2}

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

cos (t) y^{^{'}} + sin (t) y - 1 = 0

f (x) = 2 x, (1, 2)

\int \frac{4}{x ( x - 4 ) ^{2}} d x

x \to 1 + lim (arcsin (x))

What is the integral from-5 to 5 of (x-sqrt(25-x^2)) ?
The integral from-5 to 5 of (x-sqrt(25-x^2)) is -(25pi)/2