Calculus
posted by Shelby .
Find the value of a≥0 that maximizes the integral from 0 to a of (4x²)dx.
Thank you!

Calculus 
Steve
You have Int[f(x)] = F(a)
To maximize F(a), you want its derivative f(a) to be zero.
4a^2 = 0 when a = 2 or 2
Knowing what you do about cubics, you know the max on [0,4] will occur at a = 2.
Respond to this Question
Similar Questions

Calculus II/III
A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the xaxis from 4 to 9. For part … 
calculus
consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value … 
calculus
consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value … 
Math
Use the simplex method to find the maximum value of P = 3x + 3y subject to these constraints: 3x + 2y ≤ 360 x  y ≤ 60 y ≤ 120 x ≥ 0, y ≥ 0 What is the maximum value of P? 
calculus
LEt f and g be continous functions with the following properties i. g(x) = Af(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = 3A a find the … 
calculus
LEt f and g be continous functions with the following properties i. g(x) = Af(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = 3A a find the … 
math
LEt f and g be continous functions with the following properties i. g(x) = Af(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = 3A a find the … 
Calculus (pleas help!!!)
Let f(x)=e^(2x)kx, for k greater than 0. Using a calculator or computer, sketch the graph of f for k=1/9, 1/6,1/3,1/2,1,2,4. Describe what happens as k changes. f(x) has a local minimum. Find the location of the minimum. x= ____ Find … 
Calculus Please Help
Let f(x)=e^(2x)kx, for k greater than 0. Using a calculator or computer, sketch the graph of f for k=1/9, 1/6,1/3,1/2,1,2,4. Describe what happens as k changes. f(x) has a local minimum. Find the location of the minimum. x= ____ Find … 
Algebra 2
Jack is selling wristbands and headbands to earn money for camp. He earns $2 for each wristband and $3 for each headband. He wants to earn at least $50. He needs to sell at least 5 wristbands. Which system of inequalities is shown …