5.2 Integration & Anti-derivatives
Question #6 (Medium): Inequality Based on the Comparison Property of Integral
The inequality based on the comparison property of integral, where ∫
∫ ( ) ∫ , sets the lower and upper bound estimate for the integral.
It is not safe to assume that the beginningvalue of the interval ]corresponds to the absolute
minimum and the end value to the absolute maximum of ( ) . Make sure to check by taking the first
derivative of ( ), then set it to zero, such that( ) to get the critical value. Then check the
sign of ( ) with respect to the criticalvalues to see which one is the max and min value.
Estimate the integral by setting up the inequality based on the Comparison Property of Integral.
This property of integral uses the absolute min and max values over the interval ], so that:
∫ ∫ ( ) ∫ .
If familiar with the gr