April 1, 2015

Homework Help: calc: avg value

Posted by COFFEE on Monday, July 2, 2007 at 2:58pm.

Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2].

and this is what i did.. please check for mistakes. thanks :D

f(x) = x^2 sqrt(1+x^3), [0,2]
f ave = (1/(b-a))*inegral of a to b for: f(x) dx
f ave = (1/(2-0))*integral of 0 to 2 for: x^2 sqrt(1+x^3) dx
..let u = x^3 & du = 3x^2 dx
f ave = (1/2)*integral of 0 to 2 for: sqrt(1+u)*3 du
f ave = (3/2)*integral of 0 to 2 for: sqrt(1+u) du

= (3/2)[(2/3)(x+1)^(3/2)] from 0 to 2
= (3/2)[(2/3)((2)+1)^(3/2)] - (3/2)[(2/3)((0)+1)^(3/2)]
= (5.1962 - 1)
= 4.1962

For Further Reading

* calc check: average value - bobpursley, Saturday, June 30, 2007 at 6:06am

When you change variables, you have to change limits of integration. When
x=0, u=0; when x=2, u=8

That will change the answer.


How did you get u=8? wouldn't it be u=12 when x=2?

To find this don't I just plug in 2 for f(x), f(2)=(2)^2*Sqrt(1+(2)^2)) = 12
and then I would evaluate:

(3/2)[(2/3)(x+1)^(3/2)] at 0 and 12?

Please let me know if this is correct. Thanks.

NEVERMIND...dumb mistake on my part. I don't know what I was think. I know where the 0 and 8 come from. Thanks.

Answer this Question

First Name:
School Subject:

Related Questions

calc check: average value - Find the average value of the function "f(x) = x^2 ...
Calculus (Please Check my answers) - Find the average value of the function i=...
Calculus (please check my answer) - Find the Avrage value of the function i=15(1...
Math/Calculus - Solve the initial-value problem. Am I using the wrong value for ...
Calculus check - Given f(x)=4+3/x find all values of c in the interval (1,3) ...
Calc, Mean Value Theorem - Consider the function : 3x^3 - 2x^2 - 4x + 1 Find the...
calc - Verify that the function satisfies the three hypotheses of Rolle's ...
Advanced Math - Can someone check these for me? Please? Use half-angle identity ...
Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...
Calculus check - Given f(x)=x^4(2x^2-15). On what interval(s) is the graph of f ...