Difference Between Definite and Indefinite Integrals

A definite integral has upper and lower limits on the integrals, and it's called definite because, at the end of the problem, we have a number – it is a definite answer. ... Indefinite integral is more of a general form of integration, and it can be interpreted as the anti-derivative of the considered function.

1. What is definite integral?
2. What is the difference between areas and definite integrals?
3. Why is it called indefinite integral?
4. What is the primary difference between using anti differentiation when finding a definite Versus and indefinite integral?
5. Can a definite integral be negative?
6. Why do we use definite integrals?
7. Why does Antiderivative give area?
8. Can an area be negative?
9. What does an indefinite integral give you?
10. What are indefinite integrals used for?
11. What is the indefinite integral of 0?

What is definite integral?

A definite integral is an integral. (1) with upper and lower limits. If is restricted to lie on the real line, the definite integral is known as a Riemann integral (which is the usual definition encountered in elementary textbooks).

What is the difference between areas and definite integrals?

If a function is strictly positive, the area between it and the x axis is simply the definite integral. If it is simply negative, the area is -1 times the definite integral.

Why is it called indefinite integral?

2 Answers. A primitive of a function f is another function F such that F′=f. If F is a primitive of f, so is F+C for any constant C, the so called constant of integration. The indefinite integral of f can be thought of as the set of all primitives of f: ∫f=F+C.

What is the primary difference between using anti differentiation when finding a definite Versus and indefinite integral?

Indefinite integral means integrating a function without any limit but in definite integral there are upper and lower limits, in the other words we called that the interval of integration. The antiderivative of x² is F(x) = ⅓ x³.

Can a definite integral be negative?

1 Answer. Yes, a definite integral can be negative. Integrals measure the area between the x-axis and the curve in question over a specified interval. If ALL of the area within the interval exists above the x-axis yet below the curve then the result is positive .

Why do we use definite integrals?

The definite integral is defined to be exactly the limit and summation that we looked at in the last section to find the net area between a function and the x -axis. Also note that the notation for the definite integral is very similar to the notation for an indefinite integral.

Why does Antiderivative give area?

This theorem is so important and widely used that it's called the “fundamental theorem of calculus”, and it ties together the integral (area under a function) with the antiderivative (opposite of the derivative) so tightly that the two words are essentially interchangeable.

Can an area be negative?

"Areas" measured by integration are actually signed areas, meaning they can be positive or negative. Areas below the x-axis are negative and those above the x-axis are positive.

What does an indefinite integral give you?

An indefinite integral is a function that takes the antiderivative of another function. ... The indefinite integral is an easier way to symbolize taking the antiderivative. The indefinite integral is related to the definite integral, but the two are not the same.

What are indefinite integrals used for?

The indefinite integral represents a family of functions whose derivatives are f. The difference between any two functions in the family is a constant. The integral key, which is used to find definite integrals, can also be used to find indefinite integrals by simply omitting the limits of integration.

What is the indefinite integral of 0?

The integral of 0 is C, because the derivative of C is zero. Also, it makes sense logically if you recall the fact that the derivative of the function is the function's slope, because any function f(x)=C will have a slope of zero at point on the function. Therefore ∫0 dx = C. (you can say C+C, which is still just C).