# calc check: average value

posted by .

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

## Similar Questions

1. ### Calc, Mean Value Theorem

Consider the function : 3x^3 - 2x^2 - 4x + 1 Find the average slope of this function on the interval. By the Mean Value Theorem, we know there exists a "c" in the open interval (-2,3) such that f'(c) is equal to this mean slope. Find …
2. ### calc

Verify that the function satisfies the three hypotheses of Rolle's Therorem on the given interval. Then find all numbers c that satisfy the conclusiton of Rolle's Theorem. f(x)= x*sqrt(x+6) [-6,0] f is continuous and differential f(-6) …
3. ### calc: avg value

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 …
4. ### Math/Calculus

Solve the initial-value problem. Am I using the wrong value for beta here, 2sqrt(2) or am I making a mistake somewhere else?

Can someone check these for me? Please? Use half-angle identity to find the exact value of cos165 degrees. (-1/2) sqrt(2+sqrt(3)) Write the equation 2x+3y-5=0 in normal form. (-2sqrt(13)/13)x- (3sqrt(13)/13)y+ (5 sqrt (13)/13) = 0

Find the Avrage value of the function i=15(1-e to the power of -1/2 t) from t=0 and t=4?

Find the average value of the function i=15(1-e to the power of -1/2 t) from t=0 and t=4?
8. ### Calculus

Find the average value of the function f(x) 8x^2-9x+8 on the interval [3,5]. Find the value of the x-coordinate at which the function assumes it's average value The average value is ?
9. ### Calculus check

Given f(x)=4+3/x find all values of c in the interval (1,3) that satisfy the mean value theorem. A. 2 B. Sqrt(2) C. Sqrt(3) D. +or- sqrt(3) E. MVT doesn't apply I got C
10. ### Calculus check

Given f(x)=x^4(2x^2-15). On what interval(s) is the graph of f concave upwards?

More Similar Questions

Post a New Question