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Math Help - Definite integral within specified range

  1. #1
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    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?
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Mr.Ree View Post
    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???.......
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  3. #3
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    I did:

    30 (1.346)^x = 8

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

    x= -4.448300991

    How do i get a and b?
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  4. #4
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    Quote Originally Posted by Mr.Ree View Post
    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
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Mr.Ree View Post

    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?
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