Question: Suppose that (a) = (b) = g(a) = g(b) = 0 and the second derivatives of and g are continuous on the closed interval

Suppose that ƒ(a) = ƒ(b) = g(a) = g(b) = 0 and the second derivatives of ƒ and g are continuous on the closed interval [a, b]. Prove that

b b [*f(x) g(x) dx = [*1*(x)g(x) dx. f(x)g"(x) a a

b b [*f(x) g(x) dx = [*1*(x)g(x) dx. f(x)g"(x) a a

Step by Step Solution

★★★★★

3.43 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

By Parts xgx dx xgx ... View full answer

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 Calculus 10th Edition Questions!

Q:

Proof (a) Let 1 (x) and 2 (x) be continuous on the closed interval [a, b]. If 1 (a) 2 (b), prove that there exists c between a and b such that 1 (c) = 2 (c). (b) Show that...

Q:

Suppose that a B + - tree index on branch-city is available on relation branch, and that no other index is available. List different ways to handle the following selections that involve negation? a. ...

Q:

Suppose is a continuous function defined on a closed interval [a, b]. (a) What theorem guarantees the existence of an absolute maximum value and an absolute minimum value for f? (b) What steps would...

Q:

1. True / False. Every function f that is differentiable on the closed interval [ a , b ] is itself the derivative of some function g on the same closed interval [ a , b ] . Explain your reasoning if...

Q:

2. Suppose the second partial derivatives of f are continuous on a disk with center (a, b), and suppose that f, (a, b) =0 and f, (a,b) = 0. Let D(a, b) = fax (a,b) f,, (a,b) -[f, (a, b ) ]. In class...

Q:

Kindly please digitalized the answer 1- Integrate the following. 1. fx'dx 2. JT 3. S(x2 - 2x + 5) dx 4. S(x + 2)5 dx 5. S1+ y2 2ydy 6. S cos(70 + 5) do 7. S ( x2 + 2x - 3)(x + 1) dx 11- Find the Area...

Q:

KINDLY PLEASE DIGITALIZED IT 11- Find the Area between the curve y=x(x-3) and the ordinates x=0 and x=5. Note: (hint) The Graph shows 2 regions. Get first the area of each region before adding it...

Q:

Hello, can you help me out? I just really need this to learn. I would really appreciate if you would help me out. Thank you so much! ACTIVITIES Activity #1: Solve and Identify! Determine if the given...

Q:

Good day, please help me out i badly need this thank you so much! D ACTIVITIES Activity #1: Solve and Identify! Determine if the given functions f(x) are continuous or not at the given value of x....

Q:

Please make sure that your work is clearly legible and includes every steps, and then upload your written solution as a pdf or word file. 1) Use the Chain Rule to express the second derivative of f o...

Q:

True or false: ||w|| ||v|| + ||v + w|| for any v. w V.

Q:

Explain the differences among CPMs, TCPMs, and CPPs. How are they used to estimate the cost efficiency of a media plan?

Q:

Advertisers always start to give a product a useful selling price USB

Q:

b. What does the consultant do to help the presenter speak freely?

Q:

In problem, determine whether each relation represents a function. For each function, state the domain and range. {(-2, 4), (-2, 6), (0, 3), (3, 7)}

Q:

In problem, determine whether each relation represents a function. For each function, state the domain and range. {(-4, 4), (-3, 3), (-2, 2), (3, 3)}

Q:

In problem, find an equation of the line L. L is perpendicular to y = 2x (1, 2) -1 - 2xF 3

Q:

What is the firm's cash flow from investing? Answer format: Number: Round to: 0 decimal places.

Q:

Please solve by hand and not through excel (also do incremental analysis) Question 4 (25 points): Two mutually exclusive investments have the following cash flows and both need to have a minimum rate...

Q:

AutoSave OFF AA v G... Chapter 40 - Validating data template Home Insert Draw Page Layout Formulas Data Review View Tell me Share Comments X Arial V 10 V AP = = ab Wrap Text General NT LIX V Do L. 29...