Question

consider the function

f(x) = (x if x<1
(1/x if x>or equal to 1

Evaluate the definite integral:

int_{-2}^{3} f(x)\,dx =

Answer 1

You have to say what is the lower limit and what is the upper limit of your integral to do a definite integral

I guess your function is

f(x) = x for x < 1
and
f(x) = 1/x for x >/= 1

(-2)^3 = -8

so when x<1
integral = -8 [x^2/2 upper-x^2/2 lower]
and for x >/= 1
integral = -8 [ln x upper - ln x lower]

Answer 2

∫[-2,3] f(x) dx
= ∫[-2,1] x dx + ∫[1,3] 1/x dx

Now you can take it from there.

Note that f(1) is not defined.

Answer 3

technically, since f(1) is not defined, you need to take the limits as x->1, but you will wind up with the same values.

Answer 4

it saying -8 isn't the number