Algebra

Showing posts with label mean value. Show all posts
Showing posts with label mean value. Show all posts

Interactive: Mean Value Theorem for Integrals

Mean Value Theorem for Integrals: If $$f$$ is continuous on $$[a,b]$$, then there exists a number $$c$$ in $$[a,b]$$ such that $\int_a^b {f\left( x \right)dx = f\left( c \right)\left( {b - a} \right)}$

Instructions: Drag a and b to see c calculated dynamically. The area under the curve from a to b is the same as the area of the pink rectangle formed by b - a and f(c).

Interactive: Mean Value Theorem

Mean Value Theorem: Let $$f$$ be a function that satisfies the following:
• $$f$$ is continuous on a closed interval $$[a, b]$$.
• $$f$$ is differentiable on the open interval $$(a,b)$$.
Then there is a number $$p$$ in $$(a,b)$$ such that
$f'\left( p \right) = \frac{{f\left( b \right) - f\left( a \right)}}{{b - a}}$

Instructions: With the mouse, move points A and B along the function to see the Mean Value Theorem in action. Refresh browser to start over.

YouTube Video Lectures by Rob Shone