# Math Help - Definite integral within specified range

1. ## Definite integral within specified range

I am interested in finding the area under a function within the domain: -8 to 0 and the range: 0 to 8

my function is 30(1.346)^x

Integrating this with upper bounds 0, and lower bounds -8, I get 91.59

However, I am just interested in the area below y=8, since my range is only 0 to 8. How can I overcome this- its been puzzling me.

I know I'm getting this result because my y intercept is 30. but how can I get the area of the function within the domain: -8 to 0, and range: 0 to 8?

2. Originally Posted by Mr.Ree
I am interested in finding the area under a function within the domain: -8 to 0 and the range: 0 to 8

my function is 30(1.346)^x

Integrating this with upper bounds 0, and lower bounds -8, I get 91.59

However, I am just interested in the area below y=8, since my range is only 0 to 8. How can I overcome this- its been puzzling me.

I know I'm getting this result because my y intercept is 30. but how can I get the area of the function within the domain: -8 to 0, and range: 0 to 8?
You must find where the line $y=8$ intersects your curve

IE $30(1.346)^x=8$

Use these numbers (a and b respectively) as the as the upper and lower bounds. Then integrate

$\int_a^b8dx$

I think this is what you're asking???.......

3. I did:

30 (1.346)^x = 8

x = ln (4/15) / ln(1.346)

x= -4.448300991

How do i get a and b?

4. Originally Posted by Mr.Ree
I am interested in finding the area under a function within the domain: -8 to 0 and the range: 0 to 8

my function is 30(1.346)^x

Integrating this with upper bounds 0, and lower bounds -8, I get 91.59

However, I am just interested in the area below y=8, since my range is only 0 to 8. How can I overcome this- its been puzzling me.

I know I'm getting this result because my y intercept is 30. but how can I get the area of the function within the domain: -8 to 0, and range: 0 to 8?
find where the function intersects the line $y = 8$ in quad II, call that $x = a$

$A = \int_{-8}^a f(x) \, dx + \int_a^0 8 \, dx$

5. Originally Posted by Mr.Ree

How do i get a and b?

You must find where the line $y=8$ intersects your curve

IE $30(1.346)^x=8$

Can you solvw for x?