Question

can anyone answer me..the formations of definite integral of f(x) on [a,b] ?

Answer 1

insufficient information

Answer 2

i guess: let f'(x) = integral of f(x) ==> f'(x)(b-a)

Answer 3

owh...ok thanks

Answer 4

f'(x) is the derivative, not the integral

Answer 5

not if u let it = intergral :P

Answer 6

i just couldnt think of a way to represent it. i guess i should have said let g(x) = integral f(x)

Answer 7

is that the formation of definite integral? i really dont understand in...:(

Answer 8

*it

Answer 9

tbh, the question seems way to general to be a question. Is that the exact wording?

Answer 10

the question : discuss (in detail) the formations of definite integral of f(x) on [a,b].

Answer 11

Is this what you're looking for?\[\int_{a}^{b}f(x)dx=\lim_{n\to\infty}\sum_{i=1}^{n}f(c_{i})\Delta x_{i}\]

Answer 12

ya..but how to explain it?

Answer 13

Where\[\Delta x_i=\frac{b-a}{n},\]\[c_i=a+\left(\frac{b-a}{n}\right)i.\]You could use something else for the second equation above.

Answer 14

owh..thanks! you help me a lot ^^

Answer 15

You could say that the integral of a function within a range (a, b) is defined to be the summation of infinitely-many rectangles with (often) equally sized bases, which are partitions of the range (a, b), (having infinitely small length) and height defined as the function value evaluated at each partition.

Answer 16

perfect! thanks