MAT136H1 Lecture : 5.2 Integration & Anti-derivatives Definite Integrals Question #6 (Medium)

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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 beginning value 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 critical values 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: