Which of the following integrals cannot be evaluated using a simple substitution?
I think it is A because if you would substitute there would be nothing left in the equation? Is that right?
Options
∫√(x-1)
∫1/√(1-x^2)
∫x/√(1-x^2)
∫√(x^2-1)
A.
let y = x-1
dy = dx
∫√(x-1) = ∫y^.5 dy
that works
Wait so A is right or is it wrong?
B.
let y = 1 - x^2
dy = -2 x dx
∫1/√(1-x^2) dx = ∫y^-.5 dy/(-2x)
very awkward
Hey be sure to include the dx in your integrals
C will be easy because the x in -2xdx cancels
You are wrong. A CAN easily be solved
Be sure to include the dx in your integrals so you include it when you substitute
Okay will do. So I'm presuming your saying the answer is B. I think D works.
∫√(x^2-1) dx <---- NOTE that dx
let y = x^2-1
then dy = 2 x dx so dx = dy/2x
∫√(x^2-1) DX =∫y^.5 dy/2x
a mess again
I had trouble with B and D
the problem with B and D is that
dx = dy/f(x)
so the substitution does not get rid of the x