Question

Evaluate the integral
e^-0.01x-6 dx from 0 to 100

Answer 1

Is the -6 in the exponent?

Answer 2

yes

Answer 3

\[\large \int\limits_0^{100}e^{(-0.01x-6)}dx\]

Using laws of exponents, we can rewrite our exponential like so,\[\large e^{(-0.01x-6)} \qquad = \qquad e^{-0.01x}\cdot e^{-6}\]

Notice that e^{-6} is a constant with respect to x, so we can simply pull it out of the integral, giving us,\[\large e^{-6}\int\limits_0^{100}e^{-0.01x}dx\]

Understand what I did so far?

Answer 4

yes I do

Answer 5

Do you understand how to evaluate this integral?

\[\large \int\limits e^{2x}dx\]

Answer 6

I think so. Is the answer -100/e^7 + 100/e^6 ?

Answer 7

Yes, very good! :)

Answer 8

thank you!