Antiderivative Of Cosx

Page 1

Antiderivative Of Cosx Antiderivative Of Cosx The antiderivative is the name we sometimes, (rarely) give to the operation that goes backward from the derivative of a function to the function itself. Since the derivative does not determine the function completely (you can add any constant to your function and the derivative will be the same), you have to add additional information to go back to an explicit function as antiderivative.

There are set formulas that will help you find the antiderivative of your function. Many of these are listed under integrals in my reference tables. Integrals, by the way, are basically antiderivatives, set into a formula designed to tell you to take the antiderivative. So when I say take the integral I mean antiderivative, except for a whole function. And you will always have to add a " + C " afterward, because every integral has an unknown constant added to the equation. I will explain this shortly Know More About Laplace Series

Tutorcircle.com

Page No. : ­ 1/4


Antiderivative of function f is the function F whose derivative is function f. We can understand it by an equation as F'=f. This process is also known as anti-differentiation. This term is related to the definite integrals by using the functions of calculus. So Antiderivative of cos (x) is basically in form of sin (x) because derivative of sin (x) is cos (x) and as we know the antiderivative is the reverse process of differentiation. Integrals that need substitution can be fiendishly difficult. Not for me, maybe, but for most people – just a bit. The simpler substitution rules are taught in Calculus 1. I’m not sure why, since integrals are primarily in Calculus 2, but perhaps they just want you to have an introduction before you get buried in it. The substitution that you need will only become easy with practice. But there are definite rules that you should work with. ∫ (x + 2)2 dx This problem is actually not that hard, because you can foil the equation and have 3 easy terms. But let’s try to solve it in its current state. The first thing you must do is find what to substitute. This will be very similar to chain rule problems. In this function, the inside function is x + 2. If we were to replace it with u, then the function u2 has an easy integral: u3/3. But we can’t just replace. The problem that comes up is that now we will be taking the integral of a function with u, and the dx at the end says take the integral of a function with x. The rule here is that dx = du/u’. Read More About Antiderivative Of Arcsin

Tutorcircle.com

Page No. : ­ 2/4


So in the equation, replace the dx with a du divided by the derivative of you and then you can solve. After you have solved, though, remember to convert the u back to x. Anti derivative of function f is the function F whose derivative is function f. We can understand it by an equation as F'=f. This process is also known as anti differentiation. This term is related to the definite integrals by using the functions of calculus. It can be understand by an example as the function F(x)=x3/3 is an anti derivative of the function f=x2 means x2 have indefinite number of anti derivatives because the derivative of a constant is zero so x3/3+3,x3/3+78,x3/3+453 and so on. By it we can understand that when the value of the constant is changed then the new anti derivative is obtained as F(x)=x3/3+c here c is a arbitrary constant. The applications of antiderivatives is understand with an example of acceleration and velocity in physics as v=u+at ,where v and u are velocity and a is acceleration as anti derivative of this equation means Integration of the acceleration yields the velocity and a constant as: a=dv / dt + c and ∫t1t2 a(t) dt = v (t2) -v (t1) .This same pattern is applied to all other parts of equation as position ,velocity, acceleration and so on .These are some essential application of anti derivative.

Tutorcircle.com

Page No. : ­ 2/3 Page No. : ­ 3/4


Thank You

TutorCircle.com


Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.