The average value of a continuous function f(x) on the closed interval [3,7] is 12. Whats the value of ∫ from [3,7] f(x) dx?
To find the value of the integral of the function f(x) over the closed interval [3,7], we can use the average value of the function multiplied by the length of the interval.
First, let's calculate the length of the interval [3,7]. The length is given by the difference between the upper and lower limits: 7 - 3 = 4.
Next, we can calculate the value of the integral by multiplying the average value of the function by the length of the interval: 12 * 4 = 48.
Therefore, the value of the integral of f(x) over the interval [3,7] is 48.
To find the value of ∫ from [3,7] f(x) dx, we need to calculate the definite integral of the function f(x) over the interval [3,7].
Since the average value of f(x) on the interval [3,7] is given as 12, we can use this information to find the value of the integral.
The average value of a function on a closed interval can be calculated by taking the definite integral of the function over that interval and dividing it by the length of the interval. So, we have the equation:
average value = 12 = ∫ from [3,7] f(x) dx / interval length
The length of the interval [3,7] is given by the difference between the upper and lower bounds: 7 - 3 = 4.
Rearranging the equation, we get:
∫ from [3,7] f(x) dx = average value * interval length
∫ from [3,7] f(x) dx = 12 * 4
∫ from [3,7] f(x) dx = 48
Therefore, the value of ∫ from [3,7] f(x) dx is 48.