do circles ones please

Exercises 5.1 Terms and Concepts 1. Define the term "antiderivative" in your own words. 19. (sec xtanx + cscxcotx) dx . Is it more accurate to refer to "the" antiderivative of f(x) or "an" antiderivative of f(x)? 20 . Se" de f(x). 3. Use your own words to define the indefinite integral of 21. 3' dt 4. Fill in the blanks: "Inverse operations do the things in the 22. , dt 5. What is an "initial value problem"? 23 . ( 2t + 3 ) 2 dt tion. 6. The derivative of a position function is a_ func- 24. / (12 + 3 ) (1 - 21) de . The antiderivative of an acceleration function is a function. 25 . ( x x dx 3. If F(x) is an antiderivative of f(x), and G(x) is an antideriva- 26 . edx tive of g(x), give an antiderivative of f(x) + g(x). 27 . a dx Problems 28. This problem investigates why Theorem 5.1.2 states that In Exercises 9 - 27, evaluate the given indefinite integral. dx = In|x|+ c. 9 . / 3x 3 dx a) What is the domain of y = Inx? (b) Find & (Inx). 10 . x dx (c) What is the domain of y = In(-x)? (d) Find & ( In (-x) ) . (e) You should find that 1/x has two types of antideriva- 11. (10x 7 - 2) dx tives, depending on whether x > 0 or x