Saturday
March 28, 2015

Homework Help: calc check: average value

Posted by COFFEE on Saturday, June 30, 2007 at 2:56am.

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

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.

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

calc: avg value - Find the average value of the function "f(x) = x^2 sqrt(1+x^3...
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...
Calc, Mean Value Theorem - Consider the function : 3x^3 - 2x^2 - 4x + 1 Find the...
Calculus check - Given f(x)=4+3/x find all values of c in the interval (1,3) ...
Advanced Math - Can someone check these for me? Please? Use half-angle identity ...
Calculus check - Given f(x)=x^4(2x^2-15). On what interval(s) is the graph of f ...
Math/Calculus - Solve the initial-value problem. Am I using the wrong value for ...
Calculus - Find the average value of the function f(x) 8x^2-9x+8 on the interval...
calc - Verify that the function satisfies the three hypotheses of Rolle's ...

Members