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Question: How to evaluate this integral that way.

Question:How to evaluate this integral that way.

C_R 2582 Maple
integration int
June 20 2023
1

I need tutoring on some calculus basics.

y(x)

y(x)

 (1)

diff(y(x), x)

diff(y(x), x)

 (2)

(Int = int)(diff(y(x), x), x)

Int(diff(y(x), x), x) = y(x)

 (3)

(Int = int)(diff(y(x), x), x = a .. b)

Int(diff(y(x), x), x = a .. b) = int(diff(y(x), x), x = a .. b)

 (4)

The right-hand side below is the desired evaluation.

(`@`(value, rhs))(Int(diff(y(x), x), x = a .. b) = int(diff(y(x), x), x = a .. b)) = eval(int(diff(y(x), x), x), x = b)-(eval(int(diff(y(x), x), x), x = a))

int(diff(y(x), x), x = a .. b) = y(b)-y(a)

 (5)

Download Eval_definite_integral.mw

Maple does integrate the indefinite integral but not a definite version of it.

I assume that this is not possible without additional assumptions on y(x).

I tried to assume the properties continuous and differentiable.

Anything else that can be done/assumed to force evaluation the way I want?

Here is an example of how such integrals can come about
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