Math

With each of the problems include a basic sketch of the integrand function and shade the signed area represented by the integral.

1. Find

.

2. Find

.

3. Find

(The answer is a function of

http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bx%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15

).

4. Find

(

= 2.71 dots

).

5. Find

.

6. For what

is the area under the graph of

(t) = 1/t

between

= 1

and

= x

equal to

http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7B1%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15

?

7. The chance that a specific type of FLC (compact fluorescent lamp) bulb burns out within

years is given by

Calculate the chance that a given bulb lasts at least 5 years.

8. (ask, discuss - and share your ideas, but no need to submit - a great opportunity to increase your participation). A unit disk is sliced so that the smaller portion has width

. How would you set up the integral? What is the picture? Since calculating this integral can be difficult as we did not cover substitution tricks, use wolframalpha to find the antiderivative.

9. (ask, discuss - and share your ideas, but no need to submit) The graph of a function

is sketched below. (a)Without finding an antiderivative of

(x)

, calculate

ntegral from 0^1 f(x) dx

. (b) How would a graph of an antiderivative of

(x)

look like?