# Introduction to Integrals

### Problems for "Average Value and Second Fundamental Theorem"

Problem : Find the average value of f for f (x) = 3x 2 - 6x on [- 1, 1] .

Problem : Find the average value of f for f (x) = sin(x) on [- Π, Π] .

Problem : For the function above, find the c on [- Π, Π] such that f (c) = f avg

Problem : Use the second fundamental theorem of calculus to find F' .

 F(x) = (9t+9)dt

Problem : Now integrate the above expression for F and then take the derivative to find F'(x) and verify the result from the previous question.

 F(x) = (9t+9)dt

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