I need help with integral please!

Question

Is   true or false?

Answer 1

Hi Kehlani F.,

I'll assume that you know that the general form of an "indefinite" integral for the polynomial term: ax^n is (a*n)*x^(n-1) + c, where c is an unknown constant, which drops out once you evaluate the integral at the respective endpoints (i.e. perform the subtraction for value(end) - value(start)).

So what is that for your expression? You might think that a = 1, and n = -4, with end = 1, and start = -2.

But that's "leading you down the garden path"!

NOTICE that the function and its integral both blow up to infinity at x = 0. (The only strange case is for integral [x^(-1)], which has a different form, ln(x), for the integral, but you still can't integrate across (or even to) x = zero.) Therefore, even though you have an expression for the indefinite integral, you CAN'T use it to integrate across x = 0. The result would be infinity, not the result suggested!

-- Cheers, -- Mr. d.