Question: Give an example of a nonzero continuous function f on [ 0 , 1 ] such that R 1 0 f ( x ) dx

Give an example of a nonzero continuous function f on [0,1] such that R 1
0 f (x)dx =0.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

solve Solve the following. i. Give an example of a nonzero continuous function f on [0,1] such that fy fcddx =0 ii. Prove that if f is continuous on [a, b], f(x) = 0 on [a,b], and if f(c) 0 for some...

Q:

(5) (Something useful) In this problem we are going to produce an important continuous real- valued function on the Moore Plane T. For each e > 0 and x R, let B((x,0), e) be the T-basic neighborhood...

Q:

Prove that a space X is connected if and only if there does not exist a continuous function f : X {0, 1}, where {0, 1} has the discrete topology.

Q:

nx (a) Let f (0, 1) R be given by fn(x) = +1. Show that {f} converges pointwise to a continuous function f, but the convergence is not uniform. (Remark: This shows that pointwise convergence to a...

Q:

A fixed point of a function f is a number c in its domain such that f (c) = c. (The function doesn't move c; it stays fixed.) (a) Sketch the graph of a specific continuous function with domain [0, 1]...

Q:

20) Let I be an interval and let fn : I -> R for each n E N. We say that the sequence { fr } of functions converges pointwise to f : I - R on / if lim fn(x) = f(x) n-+00 for every x E I. Which of the...

Q:

A fixed point of a function f is a number in its domain such that f(c) = c. (The function doesnt move ; it stays fixed.) (a) Sketch the graph of a continuous function with domain [0, 1] whose range...

Q:

(a) Give an example of a function f R* [0, 1] such that max {f, 0} does not belong to R*[0; 1]. (b) Can you give an example of f L[0, 1] such that max{f, 0} {2 L[0, 1]?

Q:

5. Prove or disprove each of the following. State clearly Whether it is true or false. (a) (4 points) Let f : R2 > R be a continuous function having at least one point of local minimum and at least...

Q:

(a) Give an example of a random experiment, where the number of members in the sample space is 3. (b) Using Venn diagram show that (AUB) = AC B, where AC = complement of A. (c) Give a combinatorial...

Q:

Relatively few inherited forms of cancer involve the inheritance of mutant oncogenes. Instead, most inherited forms of cancer are defects in tumor-suppressor genes. Give two or more reasons why we...

Q:

Will issue 140,000 shares if it uses common stock to obtain financing, alternatively, if the corporation uses debt, assume the interest rate is 8.5%, the tax rate is 34%, and income before interest...

Q:

Your company recently introduced a new file-sharing infrastructure but not all workers are following the new document-control protocols. You're concerned that documents will be overwritten, filed...

Q:

What are some food related health care issues that inner cities are more likely to see than more affluent areas? Why are certain areas most likely to experience inadequate healthy food options than...