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R is the region bounded by the functions f(x)=7x+9​ and g(x)=7x​/5+13​/5. Find the area A of R.

User Wyll Sales
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Final answer:

To find the area of the region bounded by the functions f(x) = 7x + 9 and g(x) = 7x/5 + 13/5, find the points of intersection between the two functions and evaluate the difference of their integrals.

Step-by-step explanation:

To find the area of the region bounded by the functions f(x) = 7x + 9 and g(x) = 7x/5 + 13/5, we need to find the points of intersection between the two functions. Setting f(x) = g(x) and solving for x, we get x = 5. So the region is bounded by x = 0 and x = 5.

To find the area of this region, we need to find the difference between the integrals of the two functions f(x) and g(x) from x = 0 to x = 5. The integral of f(x) is F(x) = 3.5x^2 + 9x + C, and the integral of g(x) is G(x) = (7x^2)/10 + (13x)/5 + C. Evaluating the two integrals and taking the difference, we get the area A = F(5) - G(5).

User Lucas Josino
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