1. Evaluating /Integration

I've tried this question multiple times and keep getting the wrong answer in the textbook answer key. I was hoping someone could explain how to solve these with 'e'.

evalute: ∫(e^(x+6))dx , where 3 is the upper limit and -5 is the lower limit.

Thanks for any help.

2. Re: Evaluating /Integration

Originally Posted by dgove42
I've tried this question multiple times and keep getting the wrong answer in the textbook answer key. I was hoping someone could explain how to solve these with 'e'.

evalute: ∫(e^(x+6))dx , where 3 is the upper limit and -5 is the lower limit.

Thanks for any help.
Let $u = x+6$ therefore $du = dx$ and you limits are $u(3) = 3+6 = 9 \text{ and } u(-5) = -5+6 = 1$

$\int ^3_{-5} e^{x+6} dx = \int^9_1 e^u du$ which is common integral

3. Re: Evaluating /Integration

Originally Posted by dgove42
I've tried this question multiple times and keep getting the wrong answer in the textbook answer key. I was hoping someone could explain how to solve these with 'e'.

evalute: ∫(e^(x+6))dx , where 3 is the upper limit and -5 is the lower limit.
$\int_a^b {e^{x + 6} dx} = \left. {e^{x + 6} } \right|_a^b$