Question1: One part of the Fundamental Theorem of Calculus may be stated as shown in Figure 1 of This statement emphasizes the idea that the definite integral can be used to calculate accumulated rates of change.  Give two sample problems complete with solutions that could be used to demonstrate this particular aspect of the Fundamental Theorem.

Question2. Use the derivative formula from # 2 to prove that ln (a) + ln (b) = ln (ab).

Quote for the following – Due April 10.

Question3. The other part of the Fundamental Theorem of Calculus may be stated as shown in Figure 2 of. One use of this statement is that we can now define functions whose independent variable functions as the endpoint of a definite integral. In fact, the natural logarithm function can be defined this way.

Do the following:

a) Use this definition to find the derivative of y = ln x
b) Define the natural logarithm function in terms of the area under the curve in Figure 3