how to find definite integral
Answers
Answer:
and then finish with dx to mean the slices go in the x direction (and approach zero in width).
A Definite Integral has start and end values: in other words there is an interval [a, b].
We find the Definite Integral by calculating the Indefinite Integral at a, and at b, then subtracting:
to find definite integral refer the below example:
Example: What is
2
∫
1
2x dx
We are being asked for the Definite Integral, from 1 to 2, of 2x dx
First we need to find the Indefinite Integral.
Using the Rules of Integration we find that ∫2x dx = x2 + C
Now calculate that at 1, and 2:
At x=1: ∫2x dx = 12 + C
At x=2: ∫2x dx = 22 + C
Subtract:
(22 + C) − (12 + C)
22 + C − 12 − C
4 − 1 + C − C = 3
And "C" gets cancelled out ... so with Definite Integrals we can ignore C.
Result:
2
∫
1
2x dx = 3
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