Write a value of `intsqrt(4-x^2)\ dx`

Options

A. `(x)/(2)sqrt(4-x^(2))+2sin^(-1)""(x)/(2)+C`
B. `xsqrt(4-x^(2))+sin^(-1)""(x)/(2)+C`
C. `(1)/(2)xsqrt(4-x^(2))-2sin^(-1)""(x)/(2)+C`
D. None of these

Answer

A

Explanation

Using `int sqrt(a^(2)-x^(2))dx =(x)/(2)sqrt(a^(2)-x^(2))+(a^(2))/(2) sin ^(-1) ""(x)/(a)+C,`
`intsqrt(4-x^(2))dx=intsqrt(2^(2)-x^(2))dx=(x)/(2)sqrt(4-x^(2))+2 sin ^(-1)""(x)/(2)+C.`