Question #4f239

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Answer 1 · 2017-03-24T15:51:32

See below

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:

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