Proof f(x) + g(x) dx = f(x) dx + g(x) dx anti-derivation, Mathematics

Assignment Help:

Proof of: ∫ f(x) + g(x) dx = ∫ f(x) dx + ∫g(x) dx

It is also a very easy proof. Assume that F(x) is an anti-derivative of f(x) and that G(x) is an anti-derivative of g(x). Therefore we have that F′(x) = f(x) and G′(x) = g(x).

Fundamental properties of derivatives also give us that

(F(x) + G(x))' = F'(x) + G(x) = f(x) + g(x)

and thus F(x) + G(x) is an anti-derivative of f(x) + g(x) and F(x) - G(x) is an anti- derivative of f(x)- g(x). So,

∫ f(x) + g(x) dx = F(x) + G(x) + c =∫ f(x) dx + ∫g(x) dx

 


Related Discussions:- Proof f(x) + g(x) dx = f(x) dx + g(x) dx anti-derivation

Build an equation for a hyperboloid of two sheets, 1. Build an equation for...

1. Build an equation for a hyperboloid of two sheets with the following properties: a. The central axis of the hyperboloid is the y-axis b. The two sheets are 4 units apart, an

Measurement story problem, Seth has a pet goldfish. When he got his goldfis...

Seth has a pet goldfish. When he got his goldfish , it was only 5 centimeters long . Now it has grown to be 92 millimeters long. How many millimeters has the goldfish grown since

Differentiate inverse tangent functions, Differentiate the following functi...

Differentiate the following functions. (a) f (t ) = 4 cos -1 (t ) -10 tan -1 (t ) (b)  y = √z sin -1 ( z ) Solution (a) Not much to carry out with this one other

Estimate percent of the babies born among 6 and 8.5 pounds, 25% of babies b...

25% of babies born at Yale New Haven Hospital weigh less than 6 pounds and 78% weigh less than 8.5 pounds. What percent of the babies born at Yale New Haven Hospital weigh among 6

Cartesian Coordinates, In the view below of the robot type of Cartesian Coo...

In the view below of the robot type of Cartesian Coordinates, is not the "Z" and "Y" coordinates reversed? http://www.expertsmind.com/topic/robot-types/cartesian-coordinates-91038

Judgment sampling, Judgment Sampling Here the interviewer chooses whom ...

Judgment Sampling Here the interviewer chooses whom to interview believing that their view is more fundamental because they might be directly affected for illustration, to find

Integers satisfy the inequality, How many integers satisfy the inequality |...

How many integers satisfy the inequality |10(x+1)/x^2+2x+3|=1? Solution) first thing thats not an inequality, and second thing its very easy if thats the question. the LHS = |10/

Venn diagram, A venn diagram is a pictorial representation of the sam...

A venn diagram is a pictorial representation of the sample space of an experiment. It is usually drawn as a rectangular figure representing the sample space and it cont

Compound interest, principal=2000 rate=5% time=2 years find compound intere...

principal=2000 rate=5% time=2 years find compound interest

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd