Integration using substitution help (1 Viewer)

[akuchan]

find... (integrate symbol) x/√(x^2 - 4)
let u = x^2 - 4

answer suppose to be √(x^2 -4) + C howww x_x"

 

[pLuvia]

Let u=x²-4
du=2xdx
xdx=du/2

Then transform the variable x to u using those values.

Then integrate and your answer should be sqrt(x²-4)+C

 

[akuchan]

ohh got it now, b4 i was trying to sub x = √(u + 4) into the x on top, thx


what about... If the gradient of a curve is given by dy/dx = x / (x^2 - 1)^2 and the curve passes through (2, -1) find the equation of the curve.
i just dont know how to approach this question, havent done one like this before

 

[pLuvia]

This is easier than the last one but you will have to find the constant (C or whatever you use)

First let u=x²-1
du/dx=2x

Then transform the integration in terms of u instead of x, then you will get an answer with a constant, so then sub in those (2, -1) to get the answer

 

[akuchan]

whew finally got it thx alot