Can an integral have two answers?

On the other hand, there are no cases in which an integral actually has two different solutions; they can only “look” different. For example, x+c and x2+c cannot both be solutions to the same integral, because x and x2 don’t differ by a constant.

What are the two limits of integration?

Improper integrals the limits of integration are a and ∞, or −∞ and b, respectively.

How do you integrate two terms?

Finding the Integral of a Product of Two Functions

1. Declare a variable as follows and substitute it into the integral: Let u = sin x.
2. Differentiate the function u = sin x.
3. Substitute du for cos x dx in the integral:
4. Now you have an expression that you can integrate:
5. Substitute sin x for u:

Can you get different answers for integration?

Short Answer It is entirely possible to correctly evaluate an indefinite integral using different methods and arrive at functions which look different. However, once the constant of integration is taken into account, the functions will agree.

Can there be multiple Antiderivatives?

You can have as many examples as you like. All anti derivatives of a particular function will only differ in constant term, i.e., there will be a family of anti derivatives.

Why do we use integration?

The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus, and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others.

What is mean by integration in physics?

Integration is the reverse operation to differentiation i.e. it is the process of getting from the derivative start fraction, d, g, left bracket, x, right bracket, divided by, d, x, end fraction, equals, g, prime, left bracket, x, right bracket,dxdg(x)=g′(x) to the function g, left bracket, x, right bracket,g(x).

How are the limit of integration determined?

You must determine which curves these are (occasionally they are the same curve) and then solve each curve equation for its x value with the y value assumed. These will be the limits for your x integration for this y value. Under some circumstances the limits on x involve different curves for different y values.

Does integration have product rule?

Here, the integrand is the product of the functions x and cos x. A rule exists for integrating products of functions and in the following section we will derive it. dx = d(uv) dx = u dv dx + v du dx . Rearranging this rule: u dv dx = d(uv) dx − v du dx .

Can an integration equation have two different answers?

As such, you can get, two different answers from a projection-valued measure (depending on choice of basis), but they will always be unitarily equivalent. Originally Answered: Can integration have two answers? Yes integration can have two answers. This is so because of the constants involved in differentiation.

How do you get the same form as the first integral?

Also, as a bonus, you can get the same form as the first integral by adding and subtracting from the numerator of the fraction and then breaking that into two integrals, with the difference being that you’ll get instead of (which are more obviously the same). How do I integrate from to?

What is the meaning of as integration?

As integration means to find such a function whose rate of change wrt to change in a particular independent variable is the given function, and such a curve always exist. To prove my point, lets assume a long road with no ends (symbolizing the y-axis ie the position axis).

Why are some functions integerable and others are not?

First of all, It is a misconception that some particular functions are integerable and others aren’t. As integration means to find such a function whose rate of change wrt to change in a particular independent variable is the given function, and such a curve always exist.