Area and the Fundamental Theorem of Calculus

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Presentation transcript:

Area and the Fundamental Theorem of Calculus

1. Sketch the region whose area is represented by the definite integral. Then use a geometric formula to evaluate the integral. (Similar to p.348 #1-6)

2. Sketch the region whose area is represented by the definite integral. Then use a geometric formula to evaluate the integral. (Similar to p.348 #1-6)

3. Find the area of the region by the Fundamental Theorem of Calculus 3. Find the area of the region by the Fundamental Theorem of Calculus. (Similar to p.348 #9-16)

4. Evaluate the definite integral. (Similar to p.348 #17-38)

5. Evaluate the definite integral. (Similar to p.348 #17-38)

6. Evaluate the definite integral. (Similar to p.348 #17-38)

7. Evaluate the definite integral. (Similar to p.348 #17-38)

8. Evaluate the definite integral. (Similar to p.348 #17-38)

9. Find the area of the region bounded by the graphs of the equations 9. Find the area of the region bounded by the graphs of the equations. (Similar to p.349 #43-46)

10. Find the change in cost C, revenue R, or profit P, for the given marginal. In each case, assume that the number of units x increases by 3 from the specified value of x (Similar to p.349 #47-52)

11. Find the average value of the function on the interval 11. Find the average value of the function on the interval. Then find all x-values in the interval for which the function is equal to its average value (Similar to p.349 #53-60)

12. Find the amount of an annuity with income function c(t), interest rate r, and term T (Similar to p.349 #67-70)