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).