Example:

Extended data:

General theorem of definite integral;

1. Let f(x) be continuous on the interval [a, b], then f(x) can be integrated on [a, b].

2. If the interval f(x) is bounded on [a, b] and there are only finite discontinuous points, then f(x) can be integrated on [a, b].

3. If f(x) is monotonic in the interval [a, b], then f(x) is integrable in [a, b].

3, Newton-Leibniz formula:

If f(x) is a continuous function on [a, b] and f'(x)= f(x), then

Expressed in words: the value of the definite integral formula is the difference between the value of the original function at the upper limit and the value of the original function at the lower limit.

General derivative formula:

1, C'=0(C is a constant);

2 、( Xn)' = nX(n- 1)(n∈R)；

3 、( sinX)' = cosX；

4 、( cosX)' =-sinX；

5.(aX)'=aXIna (ln is the natural logarithm);

6 、( logaX)' =( 1/X)logae = 1/(Xlna)(a & gt； 0, and a ≠1);

7 、( tanX)'= 1/(cosX)2=(secX)2

8.、cotX)' =- 1/(sinX)2 =-(cscX)2

9 、( secX)' = tanX secX；

10 、( cscX)' =-cotX cscX；

References:

Baidu encyclopedia-definite integral