Question

another demonstration pls @Mimi_x3 and @apoorvk ? :DD

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

i think it's an easy one but please show me steps :DDD

Note: Trigonometric Substitution

Answer 1

To make the pesky radical disappear, let x=2sin(theta).

Answer 2

uh-huh...then..?

Answer 3

\[x=2\sin\theta\implies dx=2\cos\theta d\theta\]sub that in\[\int{2\cos\theta d\theta\over(2\sin\theta)^2\sqrt{4-4\sin^2\theta}}\]

Answer 4

simplify...

Answer 5

from the \(x=2\sin\theta\) sub we can infer this trianglewhich will help us determine our final expression