Question

Give the formula for a function with domain (5, ∞) that has the following properties:

• f is a positive function that is continuous on (5, ∞)
• f has an infinite discontinuity at x = 5
• the area under y = f(x) and over the x-axis (for x > 5) is equal to 7.
You must verify that the area is 7 by writing down and correctly evaluating an appropriate improper integral.

Answer 1

The area under the curve y = f(x) at x-axis, on the interval x E (5, ∞) is equal to 7.

Explanation:

Solution

Given that:

f(x) = 7√x-5

The function of domain is:

D = x-5 > 0

x>5

so,

x← (5, ∞)

Now,

(1) The sequence root function is always known as positive, i.p defined from x E (5, ∞)

i.p =√x-5

Thus,

7/√x-5 >0

Therefore f(x) = 7/√√x-5 which is a positive integer, which is defined in domain x E (5, ∞).

Each value exist a real and unique values of f(x)

Now,

The function f(x) is continuous and over the interval(5, ∞)

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