Area between curves, Mathematics

Assignment Help:

Area between Curves

In this section we will be finding the area between two curves. There are in fact two cases that we are going to be looking at.

In the first case we desire to find out the area between y = f ( x ) and y = g ( x ) within the interval [a,b]. We are also going to consider that f ( x ) ≥ g ( x ) .  Take a look at the given sketch to get an idea of what initially we're going to look at.

1897_arae between curve.png

Formula for area in this case

A = ∫ba f ( x ) - g ( x ) dx                                               (1)

The second case is almost similar to the first case.  Here we are going to find out the area between x = f ( y ) and x =g ( y ) on the interval [c,d] with f ( y ) ≥ g ( y ) .

102_area between curve1.png

In this case the formula is,

 A = ∫dc f ( x ) - g ( x ) dx                                                (2)

Now (1) & (2) are entirely serviceable formulas, though, it is sometimes simple to forget that these always need the first function to be the larger of the two functions.  Therefore, rather than of these formulas we will instead utilizes the following "word" formulas to ensure that we remember that the area is always the "larger" function minus the "smaller" function.

In the first case we will utilizes,

A = ∫ba (Upper function) - (lower function) dx   a≤x≤b    (3)

In the second case we will utilize,

A = ∫dc (right function) - (left function) dx   c≤y≤d    (4)

By using these formulas will always force us to think about what is going on with each problem and to ensure that we've got the correct order of functions while we go to utilize the formula.


Related Discussions:- Area between curves

Harmonic progression (h.p.), Three quantities a, b and c are said to ...

Three quantities a, b and c are said to be in harmonic progression if, In this case we observe that we have to consider three terms in o

Find out the probability, A speaks truth in 80% of the cases and B speaks t...

A speaks truth in 80% of the cases and B speaks truth in 60% of the cases.  Find out the probability of the cases of which they are possible to contradict each other in stating sim

Shares and dividents., how much money will required to buy 200,rupees 25 sh...

how much money will required to buy 200,rupees 25 shares at premium of rupees 2

Solution of linear equation, Solution of Linear Equation How to solve ...

Solution of Linear Equation How to solve a linear equation? Please assist me.

Derivatives, What are the ingredients of a Mathematical Model? What is a mo...

What are the ingredients of a Mathematical Model? What is a model?

In how many years is the population expected to be 42, The population of a ...

The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke 0.1t where k is a constant and t is the time in years.

Velocity problem, Velocity Problem : Let's look briefly at the velocity pr...

Velocity Problem : Let's look briefly at the velocity problem.  Several calculus books will treat it as its own problem.  .  In this problem we are given a position function of an

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