What is the integral of 20-sqrt((20)^2-x^2) ?

The integral of 20-sqrt((20)^2-x^2) is 20x-200(arcsin(1/20 x)+1/2 sin(2arcsin(1/20 x)))+C

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integral of 20-sqrt((20)^2-x^2)

\int 20 - (20)^{2} - x^{2} d x

20 x - 200 (arcsin (\frac{1}{20} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{20} x))) + C

Solution steps

\int 20 - 2 0^{2} - x^{2} d x

Simplify

= \int 20 - 400 - 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 20 d x - \int 400 - x^{2} d x

\int 20 d x = 20 x

\int 400 - x^{2} d x = 200 (arcsin (\frac{1}{20} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{20} x)))

= 20 x - 200 (arcsin (\frac{1}{20} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{20} x)))

Add a constant to the solution

= 20 x - 200 (arcsin (\frac{1}{20} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{20} x))) + C

\int (4 x^{3} + 3^{x}) d x

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

\frac{d ^{2}}{d x ^{2}} (x)

x, - x, 1, 4

sin (2 x)

What is the integral of 20-sqrt((20)^2-x^2) ?
The integral of 20-sqrt((20)^2-x^2) is 20x-200(arcsin(1/20 x)+1/2 sin(2arcsin(1/20 x)))+C