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#