Posted by Ishaan on Tuesday, February 1, 2011 at 6:21pm.
If b is a positive constant, find the average value of the function f defined by f(x) = x2 + bx + 1 on the interval [1,1]

Calculus  anon, Tuesday, February 1, 2011 at 7:40pm
f(x)= x^2 + bx + 1 on [1,1]
First, integrate
 = integration symbol
x^2 + bx + 1 = 1/3 x^3 + 1/2 bx^2 + x + C
Evaluate from 1 to 1
1/3 x^3 + 1/2 bx^2 + x + C
1/3 (1)^3 + 1/2 b(1)^2 + 1  (1/3 (1)^3 + 1/2 b(1)^2  1
1/3 + 1/2 b + 1  (1/3 + 1/2 b  1)
1/2 b + 4/3  (1/2 b  4/3) = 8/3
Average Value
V = 1/(b  a) * f(x)
V = 1/(1  (1)) * 8/3
V = 1/2 * 8/3
V = 8/6 = 4/3
Answer This Question
Related Questions
 Calculus  I'm supposed to find the average value of the function over the given...
 Calculus  Find the average value of the function defined by f(x)= x^2 sin 3 x^3...
 CALCULUs  For all x in the interval [11,13] the function f is defined by x^3(x...
 Calculus  The function defined below satisfies the Mean Value Theorem on the ...
 Calculus  Find the average value of the function f(x) 8x^29x+8 on the interval...
 Calculus  The function defined below satisfies Rolle's Theorem on the given ...
 Calculus  Let f be the function defined by f(x)= x^3 + ax^2 +bx + c and having ...
 Calculus  The function defined below satisfies Rolle's Theorem on the given ...
 Calculus  Find the average value of the function over [1,3] and all values of x...
 Calculus HELP!!!  Here is the graph. h t t p : / /goo.gl/PTc2I (spaces added at...
More Related Questions