Learning Materials
Features
Discover
Chapter 4: Q. 12 (page 362)
Show that is an antiderivative of .
It is shown that
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
For each function f and interval [a, b] in Exercises 27–33, use the given approximation method to approximate the signed area between the graph of f and the x-axis on [a, b]. Determine whether each of your approximations is likely to be an over-approximation or an under-approximation of the actual area.
left sum with
a) n = 3 b) n = 6
Approximate the area between the graph and the x-axis from x=0 to x=4 by using four rectangles include the picture of the rectangle you are using
Suppose f is a function whose average value on
is and whose average rate of change on
the same interval is . Sketch a possible graph for f .
Illustrate the average value and the average rate of change
on your graph of f.
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Find the sum or quantity without completely expanding or calculating any sums.
Given and,. Find the value of.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App