Difference between revisions of "009B Sample Midterm 1"

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== [[009B_Sample Midterm 1,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
 
== [[009B_Sample Midterm 1,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==
<span class="exam"> Evaluate the integral:
+
<span class="exam"> Evaluate the indefinite and definite integrals.
  
::<math>\int \sin^3x \cos^2x~dx</math>
+
<span class="exam">(a) &nbsp; <math>\int x^2 e^x~dx</math>
 +
 
 +
<span class="exam">(b) &nbsp; <math>\int_{1}^{e} x^3\ln x~dx</math>
  
 
== [[009B_Sample Midterm 1,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==
 
== [[009B_Sample Midterm 1,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==

Revision as of 15:04, 12 November 2017

This is a sample, and is meant to represent the material usually covered in Math 9B for the midterm. An actual test may or may not be similar.

Click on the  boxed problem numbers  to go to a solution.

 Problem 1 

Let  .

(a) Compute the left-hand Riemann sum approximation of    with    boxes.

(b) Compute the right-hand Riemann sum approximation of    with    boxes.

(c) Express    as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.

 Problem 2 

Evaluate the indefinite and definite integrals.

(a)  

(b)  

 Problem 3 

Evaluate the indefinite and definite integrals.

(a)  

(b)  

 Problem 4 

Evaluate the indefinite and definite integrals.

(a)  

(b)  

 Problem 5 

Let  .

(a) Compute the left-hand Riemann sum approximation of    with    boxes.

(b) Compute the right-hand Riemann sum approximation of    with    boxes.

(c) Express    as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.


Contributions to this page were made by Kayla Murray