Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Assignment 9 - Avg value and arc len (1 point) Find the average value of the functions on the given interval. a) Average value of f(x)=x on [5,13] :

Assignment 99 - Avg value and arc len (11 point)\newlineFind the average value of the functions on the given interval.\newlinea) Average value of f(x)=x f(x)=x on [5,13] [5,13] :

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find derivatives of sine and cosine functionsright chevron icon

Full solution

Q. Assignment 99 - Avg value and arc len (11 point)\newlineFind the average value of the functions on the given interval.\newlinea) Average value of f(x)=x f(x)=x on [5,13] [5,13] :
  1. Define formula: Step 11: Define the formula for the average value of a function on an interval [a,b][a, b].\newlineThe formula is: Average value = 1(b−a)∫abf(x) dx\frac{1}{(b-a)} \int_{a}^{b} f(x) \, dx.\newlineHere, f(x)=xf(x) = x and [a,b]=[5,13][a, b] = [5, 13].
  2. Calculate integral: Step 22: Calculate the integral of f(x)=xf(x) = x from 55 to 1313.∫513x dx=[x22]513=(1322)−(522)=(1692)−(252)=1442=72\int_{5}^{13} x \, dx = \left[\frac{x^2}{2}\right]_{5}^{13} = \left(\frac{13^2}{2}\right) - \left(\frac{5^2}{2}\right) = \left(\frac{169}{2}\right) - \left(\frac{25}{2}\right) = \frac{144}{2} = 72.
  3. Plug into formula: Step 33: Plug the integral value into the average value formula.\newlineAverage value = (1/(13−5))×72=(1/8)×72=9(1/(13-5)) \times 72 = (1/8) \times 72 = 9.

More problems from Find derivatives of sine and cosine functions

Question
Find the derivative of f(x) f(x) .\newlinef(x)=cos⁡(x) f(x) = \cos(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡(x) f(x) = \tan(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ex f(x) = e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ln⁡(x) f(x) = \ln(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡−1x f(x) = \tan^{-1}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=xex f(x) = x e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=exx f(x) = \frac{e^x}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of f(x) f(x) . \newline f(x)=e(x+1) f(x) = e^{(x + 1)} \newline f′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=x+3 f(x) = \sqrt{x+3} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the derivative of g(x) g(x). \newline g(x)=ln⁡(2x) g(x) = \ln(2x) \newline g′(x)= g^{\prime}(x) = ______
Get tutor helpright-arrow

Posted 3 months ago

View all (249)