Can integration give different answers?

We integrated the same function and got very different answers. This doesn’t make any sense. Integrating the same function should give us the same answer. In other words, if two functions have the same derivative then they can differ by no more than a constant.

How do you find integration?

The basic integration formulas for trigonometric functions are as follows.

1. ∫ cosx.dx = sinx + C.
2. ∫ sinx.dx = -cosx + C.
3. ∫ sec2x.dx = tanx + C.
4. ∫ cosec2x.dx = -cotx + C.
5. ∫ secx.tanx.dx = secx + C.
6. ∫ cosecx.cotx.dx = -cosecx + C.
7. ∫ tanx.dx =log|secx| + C.
8. ∫ cotx.dx = log|sinx| + C.

How do you integrate a function?

How to Integrate Compositions of Functions

1. Declare a variable u and substitute it into the integral:
2. Differentiate u = 4x + 1 and isolate the x term. This gives you the differential, du = 4dx.
3. Substitute du/4 for dx in the integral:
4. Evaluate the integral:
5. Substitute back 4x + 1 for u:

What is integration of constant?

In calculus, the constant of integration, often denoted by , is a constant term added to an antiderivative of a function to indicate that the indefinite integral of (i.e., the set of all antiderivatives of. ), on a connected domain, is only defined up to an additive constant.

Can an integral have 2 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 some questions about integration with solutions?

Questions on Integration with Solutions 1 Integrate 1/ (1+x2) for limit [0,1]. Solution: 2 Find the value of ∫2x cos (x2 – 5). Solution: Let, I = ∫2xcos (x 2 – 5).dx Let x 2 – 5 = t ….. (1) 2x.dx =… 3 What is the value of ∫ 8 x3 dx. Solution: ∫ 8 x 3 dx = 8 ∫ x 3 dx = 8 x 4 / 4 + C = 2 x 4 + C 4 Find the value of ∫ Cos x + x dx. More

Are there any integration questions for Class 11?

Integration questions with answers are available here for students of Class 11 and Class 12. Integration is an important topic for 11th and 12th standard students as these concepts are further covered in higher studies. The problems provided here are as per the CBSE board and NCERT curriculum.

How to calculate the indefinite integral in problem 1?

The Indefinite Integral In problems 1 through 7, find the indicated integral. 1. R √ xdx Solution. Z √ xdx = Z x1 2dx = 2 3 x3 2+C = 2 3 x √ x+C. 2. R 3exdx Solution. Z 3exdx =3 exdx =3e +C. 3. R (3×2− √ 5x+2)dx Solution. Z (3×2− √ 5x+2)dx =3 Z x2dx− √ 5 Z √ xdx+2 Z dx = =3· 1 3 x3− √ 5· 2 3 x √ x+2x+C = = x3− 2 3 x √ 5x+2x+C. 4. R ³ 1 2x −2 x2+ √3 x

Which is the representation of the integration of a function?

Learn Integration Rules here. The representation of the integration of a function is ∫f (x) dx. The common formulas used to solve integration problems are given below in the table. Here are some questions based on the integration concept with solutions. 1. Integrate 1/ (1+x2) for limit [0,1].