Vault Of Euclid

Finding a Parameter Given the Average Value of a Polynomial

The definite integral warmup

If the average value of \( f(x) = x^{3}+bx-2 \) on \( [0, 2] \) is 4, find \( b \).

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

The definition of the average value of a function on an interval
The power rule for integration
Evaluating definite integrals of polynomials

What this problem tests

Tests the ability to set up an equation using the average value formula and solve for an unknown constant after evaluating a definite integral.

This is a standard Calculus I problem testing the understanding of the average value formula and basic integration techniques.

More on The definite integral

← today's set