MAT136H1 Lecture : 5.3 Integration & Anti-derivatives The Fundamental Theorem of Calculus Question #4 (Medium)
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Question #4 (medium): finding the derivative of the function. Notice that the fundamental theorem of calculus part 1 has ( ) ( ) from a numeric value of to a variable . This means that only one endpoint of the interval is a variable. , where the integral goes: one end containing a more complex function instead a simple : then use leibniz notation and substitute a simpler variable. Apply the chain rule in conjunction with the fundamental. Theorem of calculus part 1 to find the derivative of the function: both ends of the integral contain some kind of variable expression: then split the integral into two with usually as an easy dividing point, then proceed. Recall leibniz notation of the fundamental theorem of calculus part 1. Here only one end of the interval contains a variable, so chain rule is needed. Rearranging gives is ( ) ( ) .
