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).

0,0

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a

b

∫ = 14.6250

c

∫ = 14.6250