Question

Find the average f(x)=-(1)/(x+3);[-1,1]

Answer 1

To find the average of the function f(x) = -(1)/(x+3) over the interval [-1,1], the average is -1/3.

Step-by-step explanation:

To find the average of the function f(x) = -(1)/(x+3) over the interval [-1,1], we need to evaluate the definite integral of f(x) over that interval and divide it by the length of the interval. The average can be calculated using the formula:

Average = (1/length of interval) * ∫(lower limit to upper limit) f(x) dx

For the given function f(x) = -(1)/(x+3), the average can be found by evaluating the definite integral:
Average = (1/2) * ∫(-1 to 1) -(1)/(x+3) dx

By simplifying the integral and performing the calculations, the average of f(x) over the interval [-1,1] is:

Average = -1/3