Anti Derivative Chain Rule Anti Derivative Chain Rule
( g ( x) ) ( g(x) ) ( g'(x) ) dx = n +1
n +1
The easiest antiderivative rules are the ones that are simply the reverse of derivative rules n that you probably already know. These rules are automatic, one-step antiderivatives, with the exception of the reverse power rule, which is only slightly harder.
+C
You know that the derivative of sinx is cosx, so reversing that tells you an antiderivative of cosx is sinx. What could be simpler? Actually, there is one very little twist. Again, the derivative of sinx is cosx, but the derivative of sinx + 10 is also cosx, as is the derivative of sinx plus any constant C. So, since the derivative of sinx + C is cosx, the antiderivative of cosx is sinx + C. In symbols, Especially when you’re new to antidifferentiation, it’s a good idea to test your antiderivatives by differentiating them — you can ignore the C. If you get back to your original function, you know your antiderivative is correct. Know More About: Antiderivative of Secxtanx
Tutorcircle.com
Page No. : 1/4
In calculus, an antiderivative, primitive integral or indefinite integral[1] of a function f is a function F whose derivative is equal to f, i.e., F ′ = f.[2][3] The process of solving for antiderivatives is called antidifferentiation (or indefinite integration) and its opposite operation is called differentiation, which is the process of finding a derivative. Antiderivatives are related to definite integrals through the fundamental theorem of calculus: the definite integral of a function over an interval is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval. The discrete equivalent of the notion of antiderivative is antidifference. Example:The function F(x) = x3/3 is an antiderivative of f(x) = x2. As the derivative of a constant is zero, x2 will have an infinite number of antiderivatives; such as (x3/3) + 0, (x3/3) + 7, (x3/3) − 42, (x3/3) + 293 etc. Thus, all the antiderivatives of x2 can be obtained by changing the value of C in F(x) = (x3/3) + C; where C is an arbitrary constant known as the constant of integration. Essentially, the graphs of antiderivatives of a given function are vertical translations of each other; each graph's location depending upon the value of C. In physics, the integration of acceleration yields velocity plus a constant. The constant is the initial velocity term that would be lost upon taking the derivative of velocity because the derivative of a constant term is zero. This same pattern applies to further integrations and derivatives of motion (position, velocity, acceleration, and so on).
Read More About: Antiderivative of Log
Tutorcircle.com
Page No. : 2/4
Techniques of integration Finding antiderivatives of elementary functions is often considerably harder than finding their derivatives. For some elementary functions, it is impossible to find an antiderivative in terms of other elementary functions. See the article on elementary functions for further information. Antiderivatives are also called general integrals, and sometimes integrals. The latter term is generic, and refers not only to indefinite integrals (antiderivatives), but also to definite integrals. When the word integral is used without additional specification, the reader is supposed to deduce from the context whether it is referred to a definite or indefinite integral. Some authors define the indefinite integral of a function as the set of its infinitely many possible antiderivatives.
Tutorcircle.com
Page No. : 2/3 Page No. : 3/4
Thank You
TutorCircle.com