Question

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Evaluate the definite integral :-

$\bf{\pink{\int{\frac{1}{\sqrt{4-{x}^{2}}}}\:\:dx}}$

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Answer 1

Answer:

follows

Step-by-step explanation:

int 1 sqrt 4-x^ 2 dx= 1 2 int 1 sqrt 1- 1 4 x^ 2

Let^ prime s u= 1 2 x so u^ 2 = 1 4 x^ 2 anddu = 1/2 * d * x

The integral become

int 1 sqrt 1-u^ 2

This is the derivative f * arcsin(u)

[arcsin(u)] + C substitute back for u = 1/2 * x

[arcsin(1/2 * x)] + C