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Determine the area, in square units, of the region bounded above by f(x)=11x−3 and below by g(x)=10x−5 over the interval [12,34]. Do not include any units in your answer.

Respuesta :

Using integrals, it is found that the area bounded by the two curves in the interval is of 550 units squared.

How is the area under a graph found?

  • The area under the graph of a curve bounded above by a function f(x) and below by a function g(x) over an interval [a,b] is given by:

[tex]A = \int_a^b f(x) - g(x) dx[/tex]

In this problem:

  • The functions are [tex]f(x) = 11x - 3, g(x) = 10x - 5[/tex].
  • The interval is [12, 34], hence [tex]a = 12, b = 34[/tex].

Then:

[tex]A = \int_{12}^{34} 11x - 3 - (10x - 5) dx[/tex]

[tex]A = \int_{12}^{34} x + 2 dx[/tex]

[tex]A = \frac{x^2}{2} + 2x|_{x = 12}^{x = 34}[/tex]

Applying the Fundamental Theorem of Calculus:

[tex]A = \frac{34^2}{2} + 2(34) - \frac{12^2}{2} - 2(12) = 550[/tex]

The area is of 550 units squared.

To learn more about integrals and the calculation of area, you can take a look at https://brainly.com/question/26142669

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