Integration Basics
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Test: Integration Basics (No Calculator Permitted)
1. Evaluate 
.
2. Evaluate 
.
3. Evaluate 
.
4. Consider the summation formula
a. Write a formula for
that does not involve summation notation.
b. Use the formula from (a) to evaluate
5. The graph of
is shown above. Let R be the region bounded by f,
the vertical lines 
and 
, and the x-axis, as shaded in the figure above.
- Estimate the area of R using a lower sum of four
subintervals of equal width.
- Estimate the area of R using an upper sum of four
subintervals of equal width.
- Estimate the area of R using a midpoint sum of
four subintervals of equal width.
- Find the exact area of R using the limit process.
6. Evaluate 
.
7. Given the following information,
- Evaluate
- Evaluate
- Evaluate
Test: Integration Basics (Calculator Permitted/Required)
8. A car sits at an intersection at a dead stop. As soon as
the light turns green, the car begins to accelerate at a constant rate of 1.273
meters per second per second. Assuming that the car is able to maintain this
constant acceleration and that 
(measured in seconds) corresponds to the instant at which the
car begins to accelerate, answer the following questions.
- At what time t will the car be
meters beyond the intersection?
- How far beyond the intersection will the car be at time
? Indicate units of measure.
- At what velocity will the car be traveling at time
? Indicate units of measure.
- What is the average velocity of the car from time
to time
15? Indicate units of measure.
- At what time
, 
, is the instantaneous velocity of the car equal to the
average velocity found in part (d)?
9. Use a Riemann Sum of four subintervals to estimate
, given the following information:
10. Above, the graph of a function g is drawn. The
graph of g consists of 3 line segments and two quarter circles. Based on
the graph above, evaluate the following definite integrals:
a) 
b)
c)
d) 
11. Consider the differential equation
.
- On the set of axes provided, sketch a slope field for
the given differential equation at the 12 indicated points.
- On the same set of axes, sketch the particular solution
to the given differential equation that passes through the point
.
- Find the particular solution
to the differential equation with the initial condition
that 
.
