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hi sis to phr is ka kya solution ho ga????

In definite integrals we don't involve constant of integration because definite integral gives us a definite value at the point of calculation .In it we use two limits as a and b which is area under the curve .Definite integral has limits and numbers above and below the integral sign but in indefinite integrals which is unlimited or boundless we always add an unknown constant which is constant of integration because the derivative of F(x)+C is equal to the derivative of F(x).


The definite integral of a function is closely related to the anti derivative and indefinite integral of a function. The primary difference is that the indefinite integral, if it exists, is a real number value, while the latter two represent an infinite number of functions that differ only by a constant. The relationship between these concepts is will be discussed in the section on the Fundamental Theorem of Calculus, and you will see that the definite integral will have applications to many problems in calculus.

The indefinite integral of a function f(x) is an anti-derivative. It is a function F(x) whose derivative is f(x). You always add an unknown constant to the indefinite integral because the derivative of F(x) plus any constant is the same as the derivative of F(x).

 

The definite integral of f(x) between two limits a and b is the area under the course from x=a to x=b. it is a number, not a function, equal to F (b) – F (a).

 

Definite integral has bounds (little numbers above and below the integral sign) whereas an indefinite integral is boundless and when you integrate it you have to put a + C (constants).

The definite integral of a function is closely related to the anti-derivative and indefinite integral of a function. The primary difference is that the indefinite integral, if it exists, is a real number value, while the latter two represent an infinite number of functions that differ only by a constant.

  • integral is inverse of derivation so something lost in derivation is a constant

  • If you think of the definite integral as the area under a curve y = f(x), and above the x-axis, between certain vertical lines (two values of x), it is obvious that the area has a certain specific value, so that no "plus C" would be appropriate.

  • On the other hand, if the vertical side boundaries of the area have not yet been specified, all you've found is the "antiderivative" F(x) of the function y = f(x), and it is obvious that the derivative of F(x) + 0.776 will be the same as the derivative of F(x) + 126.72 (I made up those numbers)

Discuss the role of constant of integration in indefinite integrals, why we don't involve it in definite integrals? (Be precise)

I'm assuming you're referring to the constant that is added after integration, rather than a constant term while integrating.

The constant is added because it denotes all possible anti derivatives. For example, integral of 1 is x + c. The c can be 2, pi, 46.2 etc. The family of anti derivatives is represented using that constant c.

The indefinite integral of a function f(x) is an anti-derivative. The definite integral of f(x) between two limits and b is the area under the course from x=a to x=b. it is a number, not a function, equal to F (b) – F (a).In definite integrals we don't involve constant of integration because definite integral gives us a definite value at the point of calculation .In it we use two limits as a and b which is area under the curve .Definite integral has limits and numbers above and below the integral sign but in indefinite integrals which is unlimited or boundless we always add an unknown constant which is constant of integration because the derivative of F(x)+C is equal to the derivative of F(x).

The definite integral of a function is closely related to the anti derivative and indefinite integral of a function. The primary difference is that the indefinite integral, if it exists, is a real number value, while the latter two represent an infinite number of functions that differ only by a constant. The relationship between these concepts is will be discussed in the section on the Fundamental Theorem of Calculus, and you will see that the definite integral will have applications to many problems.

It is a function F(x) whose derivative is f(x). You always add an unknown constant to the indefinite integral because the derivative of F(x) plus any constant is the same as the derivative of F(x). 

this is the precise solution but be sure to change it in your own words and not just copy and paste this might or might not be accurate but there s always risk when you aint a mathematician yourself 

>>>>As we know that derivative of a constant is Zero, so any constant might be added to an Indefinite Integral(and will correspond to the same integral). In other words it can also be said as that the anti derivative is a non-unique inverse of a derivative and for this reason a random constant is added commonly known as Constant of Integration.

This Constant is used to express the vagueness inherent during construction of anti derivative. This generally solves the possibility for the variable in an equation. Integration is the reversing of the differences but this is not used in the case of definite integrals as they contain variables so the equation can be solved without the need of a constant to find any possibilities.

mir ali Thanks for sharing 

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