Question

Question #4f239

Answer 1

See below

Explanation:

Well they've guided you here to a solution. This assumes you know how to process a substitution:

We have:

`int1/sqrt(1-4x^2) dx`

And we're saying let `2x = cos u implies 2 dx = - sin u \ du`

So subbing this in:

`int1/sqrt(1-4((cos u)/2)^2) (- sin u \ du)/2`

`=-1/2 int1/sqrt(1-cos^2 u) cdot sin u \ du`

`=-1/2 int1/(sin u) cdot sin u \ du`

`=-1/2 int \ du = - 1/2u + C`

We now reverse the sub so we get back to `x` as the independent variable:

`2x = cos u implies u = cos^(-1) 2x`

So the final answer is:

`-1/2 cos^(-1) 2x + C`