Question

a general integration question

Answer 1

i was given an inegration formula in a test review last night that concerns integration of a constant to a power\[\int\limits a^u du=(1/Lna) a^u+c\] I later found that the constant has to be positive and not equal to one. What do you do for the integration of a constant to a power when the constant is less than zero or equal to one?

Answer 2

if less than zero..you uhhh..i dont think that's possible is it o.O

Answer 3

Any examples?

Answer 4

not sure of an example, just trying to reason out what i would do in the case that it was negative or equal to one

Answer 5

Like when you use the general power rule for integration if the power of the exponent is negative one the rule doesn't apply, what do you do then? I have learned that you then use the natural log definition of 1/u du = lnabsikute valeu of u plus c

Answer 6

A negative one do you mean like:
\[\large\int e^{-2x+1} dx\]?

Answer 7

e isnt -1 :P

Answer 8

He said raised to the negative; \(-2x+1\) is negative. :P

Answer 9

no he means when a is 1 or negative because ln of nega doesnt exist and 1/ln1 = undefined

Answer 10

lol, woops; i read it wrongly. Are you able to give an example?:P

Answer 11

in teh definition I was talking about the "a" so the constant could not be negative one or equal one. I truly haven't run into this situation, but I have had this professer three times and when she stresses a point, it is generally on the final. She stressed this rule even though we haven't been subjected to any of its content yet

Answer 12

You would have to use complex numbers (with sqrt(-1) )

Answer 13

ok thanks guys