What is the difference between and definite and indefinite integral, the graphical interpretation of the definite...

What is the difference between and definite and indefinite integral, the graphical interpretation of the definite integral and the connection between the summation approximations. (left, right, trapezoid) with the definite integral.

Expert Solution

Indefinite integral: 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). With an indefinite integral there are no upper and lower limits on the integral here, and what we'll get is an answer that still has x's in it and will also have a Gas constant.

Definite integral : The definite integral of f(x) between two limits a and b is the area under the curve from x = a to x= b. It is a number, not a function, equal to F(b) - F(a).

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.

milcah answered 2 years ago

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