MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 1,600 off
USE CODE: chait6

				   why we use calculus
				   

6 years ago

Share

Answers : (1)

										

Dear Suyash


Differential calculus can be used for finding the local slope and curvature of a function and important points on a curve: maximum, minimum, inflection points, etc. These points and slopes can be the solution to a wide variety of problems related to physics, mechanical and electrical design, perhaps chemistry and other fields where a problem can be represented by an equation with variables. One example, if you can derive total fuel consumption as a function of acceleration there may be a minimum point of the function that allows you to reach your target speed with the least fuel - this is especially important with airplanes and rockets.

Integral calculus can be used to find the area under curves which can represent the amount of work done, distance gone, energy exerted, stress, angle and deflection of beams and a host of other scientific and mechanical properties that can be characterized by equations.

One overly simple example: if I push on a 1 Kg rock in space with a constant force of "A" newtons in the same direction where A represents a constant.

The acceleration (a) as a function of time: a = A meters per second squared. The graph will be a horizontal line with respect to time (t).

The speed (v for velocity) is the integral of the acceleration: v = A * t + B where t is time (how many seconds) and B is the speed it was going when we started. At+B is the integral of A with respect to time. The graph will be a line sloping upward with slope of A units with respect to t.

The distance traveled is the integral of the speed. One half A * t squared + B * t + C where C is how far away it was when we started. ( .5At^2 + Bt + C) The graph will be a parabola with increasing slope with respect to t.

Now, if a rocket starts with a mass of 60,000 Kg of which 50,000 is fuel and uses 500 Kg of fuel per second and the force generated by the fuel burn increases with altitude up to 15,000 m and decreases thereafter and the air resistance goes up with speed and down with altitude, you will need some calculus to determine how fast it will be going and how far it has gone when it runs out of fuel.


 


 


All the best.                                                           


AKASH GOYAL


AskiitiansExpert-IIT Delhi


 


Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.


Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.


Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..


 


 



6 years ago

Post Your Answer

Other Related Questions on Integral Calculus

what is integration? and what is the real life applications of an integration?
 
 
Dear Sudharshan Integration is the one symboll used in solving problems . Integration is opposite to differentiation. It is usefull in mathematics, physics and chemistry
 
Prabhakar ch one year ago
 
DEAR SUDARSHAN, Integration is the act of bringing together smaller components into a single system that functions as one. Integration is used to compute such things as the areas and volumes...
 
naresh raju one year ago
 
dear sudarshan..... Integration is a way of adding slices to find the whole. Integration can be used to find areas, volumes, central points and many useful things. But it is easiest to start...
 
mohan one year ago
integral of sin with respect to x
 
 
Its −cosx(minus sign is also there).PLZ approve .
 
Nikhil Upadhyay one year ago
 
integral sinx = -cosx
 
sri tanish one year ago
 
∫sinx.dx=-cosx+c
 
Shantanu Singh one year ago
∫(1/sinx)dx
 
 
1/sinx =cosec x or integration of 1/x = ln |x|+c where c is arbitari constant so by using this formula integration of i/sinx is ln |sinx +c|
 
kalyan 6 months ago
 
sorry made a mistake currect answer is 1/sinx =cosec x integration of cosec(x) is ln|cosec x-cot x|+c where c is arbitari constant....
 
kalyan 6 months ago
 
1/sin(x)=cosec (x) the integration of cosec(x) is ln|cosec x-cot x|+c where cis an arbitrary constant
 
SREEKANTH 6 months ago
If alpha is a real root of the equation ax 2 +bx+c and beta is a real root of equation -ax 2 +bx+c. Show that there exists a root gama of the equation (a/2)x 2 +bx+c which lies between alpha...
 
 
 
Ajay 6 months ago
 
Small Mistake in last para posting again..............................................................................................................
 
Ajay 6 months ago
 
We have Similarly, So if P(x) = a/2 x 2 +bx +c, then and are off opposite sign and hence there must exist a root between the two numbers.
 
mycroft holmes 6 months ago
In the listed image can you tell me how beta*gamma = 2 ….. . . .. ??
 
 
The value of gamma is still not correct, either printing mistake or you gave me wrong value. The correct value of gamma is below
 
Ajay 5 months ago
 
Thankyou so much............................. …......................................................................!
 
Anshuman Mohanty 5 months ago
 
Yes sorry..... . . . .it is not so clear.. ok the values are beta = α + α^2 + α^4 and gamma = α^3 + α^5 + α^7
 
Anshuman Mohanty 5 months ago
if |z - i| Options: a*) 14 b) 2 c) 28 d) None of the above
 
 
If |z-i| = ?? PLs complete the question
  img
Nishant Vora one month ago
 
Got it! [z + 12 – 6 i ] can be rewritten as [ z – i + 12 – 5 i] => | z – i | and => |12 – 5 i | = sqrt ( 12^2 + 5^2) = 13......................(2) => | z + 12 – 6 i | => | z + 12 – 6 i |...
 
Divya one month ago
 
I tried posting the question several times, it kept cutting off the rest of the question. Here: If | z-1| Options: a*) 14 b) 2 c) 28 d) None of the above
 
Divya one month ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 6,000 off
USE CODE: chait6

Get extra R 1,600 off
USE CODE: chait6

More Questions On Integral Calculus

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details