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In each integration problem sketch for yourself a corresponding graph to ensure that your answer is reasonable.

1. Evaluate the area under the graph of = root(3)*(x)above the X-axis between = 27and = 81?

2. Evaluate the definite intergral ntegral from (-2)^8 |x| dx.

3. Evaluate the definite intergral ntegral from (1)^8[x+x^2]/[x^4] dx.

4. (a) Find the average value of os ton the intervals 0, pi], 0, pi/2],0, pi/4],0,0.01]. (b) Determine the general formula for verline (f)_([0,x])the average of os tover the interval 0,x]. (c) Calculate imit as (x to 0) overline (f)_([0,x]).

5. Evaluate the definite intergral ntegral from (0)^(pi/3) (sec^2 x+3 x)dx.

6. Evaluate ntegral from 0^pi | cos s| ds.

7. Find the general antiderivative nt x^(-2/3) dx.

Then verify by differentiation that your answer is correct.

8. Let ttp://calculus.sfsu.edu/latexrender/pictures/7792b30d26d3387765792ef87695fa6f.png

Sketch by hand a graph of = f(t). Let (x) = integral from (-1)^x f(t) dtbe defined for 2 leq x leq 4. Using FTC find '(x). Then determine the sign of '(x)and find intervals on which (x)is increasing and intervals on which (x)is decreasing. Find the minimum and maximum of (x). Check your answer by interpreting (x)as the area bounded by the graph of (t).

9. The velocity of an object moving along a straight line is (t) = t^2-10 t+16. Find the displacement over the time interval 1, 7]. Find the total distance traveled by the object.