Find the average value of the function f(x) = 6x³ on the interval 1 ≤x≤3
Answers
Answer:60
Step-by-step explanation:
To find the average value of a function on a given interval, we need to find the definite integral of the function over that interval and divide it by the width of the interval.
In this case, we are given the function f(x) = 6x³ and the interval 1 ≤ x ≤ 3. To find the definite integral of f(x) over the interval [1, 3],
we can use the power rule of integration.
First, we integrate each term of the function. The integral of x^n is (1/(n+1)) * x^(n+1).
Integrating 6x³ term by term, we get: ∫(6x³) dx = 6 * ∫(x³) dx = 6 * (1/4) * x^4 + C
Now, we evaluate the definite integral by substituting the upper and lower limits of the interval: ∫[1, 3] (6x³) dx = [6 * (1/4) * x^4] evaluated from 1 to 3 = 6 * (1/4) * 3^4 - 6 * (1/4) * 1^4 = 6 * (1/4) * 81 - 6 * (1/4) * 1 = 6 * 81/4 - 6/4 = 486/4 - 6/4 = 480/4 = 120
The definite integral of f(x) = 6x³ over the interval [1, 3] is equal to 120.
To find the average value of the function, we divide the definite integral by the width of the interval: Average value = (1/(b - a)) * ∫[a, b] f(x) dx
In this case, a = 1 and b = 3, so the width of the interval is 3 - 1 = 2.
Average value = (1/2) * 120 = 60
Therefore, the average value of the function f(x) = 6x³ on the interval 1 ≤ x ≤ 3 is 60.
Related Questions
The data set represents a progression of hourly temperature measurements. Use a graphing calculator to determine the quadratic regression equation for this data set.I've tried all of these answers but none of them seemed correct
Mr. Johnson bought 1.8 pounds of grapes for $2.20 per pound. How much did the grapes cost Mr. Johnson to purchase?A. $3.96B.$3.80C.$0.40D.$5.40
A doctor is examining three patients. Which sysmptoms do all three patients have in common?A) {headaches, hair loss, congestion}B) {cold sweats, congestion, memory loss}C) {spasms, memory loss, appetite}D) {fever, joint pain, tiredness}
Your company spends 15% of their budget on rent each year. Their operating budget was $45,000.
B. It contains different wavelengths of visible light.
C. It allows light waves to be transmitted.
D. It contains all waves on the electromagnetic spectrum.
Answers
When white light strikes any object that reflects any wavelength of visible light, that object appears to be the color that it reflects.
Answers
Below is similar question:
48 out of 100 private buses usually run on time. Out of the buses that are on time, only 36 are owned by Jerry. Out of the remaining 52 buses that usually run late, only 7 are owned by Jerry. What is the probability that a bus is owned by Jerry, given that it runs on time?
A. 0.58
B. 0.67
C. 0.75
D. 0.81
The answer is C as 36/48 = .75
Based on the number of buses owned by Jerry that usually run late, the probability that a bus owned by Jerry would run late is 13.5%.
What is the probability that Jerry's bus would run late?
This can be found as:
= Number of buses that Jerry owns which run late / Total number of buses that run late
Solving gives:
= 7 / 52
= 13.5%
Find out more on probability at brainly.com/question/20900544.
#SPJ5
Answers
perimeter = 2(l + w) = 2(3x + x) = 2(4x) = 8x = 16
x = 16/8 = 2 feet
l = 3x = 3 * 2 = 6 feet
2) 21,23,36,37,44,48,50
3) 10,19,22,23,23,29,44
4) 42,47,49,50,52,59,60
Answers
2) 48-23= 25
3) 29-19= 10
4) 59-47= 12
Test score will decrease because the graph shows negative association
Test score will increase because the graph shows positive association
Test score will increase because the graph shows negative association
Test score will decrease because the graph shows positive association
4 graphs are shown:
Which graph represents a positive nonlinear association between x and y?
Graph A
Graph B
Graph C
Graph D
Answers
Answer:
1)
Test score will decrease because the graph shows negative association.
2)
Graph A
Step-by-step explanation:
1)
Clearly from the graph we could observe from the scatter plot that:
Test score will decrease because the graph shows negative association.
( As the points or the test scores are decreasing with the increasing number of hours spent on playing games online)
2)
Positive Nonlinear association:
A positive Non-linear relationship between two variables can be shown with an upward-sloping curve in a graph.
Hence, Graph A represents the following relationship.
( Since graph B and D are linear and graph C is negative association since the value keeps on decreasing)
Test score will decrease because the graph shows negative association
Test score will increase because the graph shows positive association
Test score will increase because the graph shows negative association
Test score will decrease because the graph shows positive association
The correct answer is : Test score will decrease because the graph shows negative association.
Fact : Playing video games is a distraction and many kids fail there grade. Therefore test scores will decrease.
Part 2 : Non Linear: This can be defined as if all the points on the scatter diagram tends to lie near a smooth curve, the correlation is said to be non linear.
Answer = Diagram C
Answers
7
Explanation:
We are given the equation:
We want to get the value of the equation at c = 8.
Therefore, all we have to do is substitute c in the equation with 8 and solve as follows:
=
The 8 in the numerator will be cancelled out with the 8 in the denominator leaving us with only the 7 as a solution
Hope this helps :)
Answer:
Value is 7
Step-by-step explanation:
We are given the expression, .
It is required to evaluate the expression for c= 8.
So, after substituting the value of c= 8 in the given expression, we get,
=
= 7
Hence, the value of the expression at c= 8 is 7.