INTEGRATION OF STUFF

Question

Is this convergent or divergent? If it is convergent can you evaluate it?

∫ top limit = 1 and bottom is - oo 7/ (2x-3)^2 dx

Answer 1

Remember that if you use the substitution method, you should get ∫7p^--2 dp

where p = (2x -3), so you should see that the integral converges. The important step to evaluate is to now change the bounds of integration

x = 1 gives p = 2 -3 = -1 and x = ∞ gives p = 2(∞)-3 = ∞

The infinity means you should evaluate the function you get as the integral as a limit so you should have

lim _x→∞ (7[]_x) - 7[]₁