The definite integral of periodic function on (a, a + T) has nothing to do with A. how to prove it? The definite integral of periodic function on (a, a + T) has nothing to do with A. how to prove it? F (x) = f (x + T). Find the definite integral of F (x) on [a, a + T]. The conclusion is that the definite integral is a definite value, that is, the definite integral of F on [0, t].

The range of substitution x = y + a into (0, t) is independent of A
But still don't understand the meaning of the landlord

If the definite integral of a continuous periodic function in one period is equal to 0, then there are two roots in any period. Why,
When f (x0) is not equal to 0, there must be at least two roots in (x0, x0 + T)

Because it's a continuous periodic function
F (x0) = f (x0 + T), f (x0) is not equal to 0
That is, f (x0), f (x0 + T) have the same sign
And the definite integral is zero
There must be a value different from F (x0), f (x0 + T) sign in the interval
If there is Rolle's theorem, there must be two or more roots

A property of definite integral of periodic function is not clear
Theorem 3.7 assumes that the function f (x) has a period T, that is, for any real number x, f (x + T) = f (x) is integrable on [0, t], then
(1) ∫ upper limit a + T, f (x) of lower limit a = ∫ upper limit t, f (x) DX of lower limit o (this understanding)
(2) The necessary and sufficient condition for the f (T) DT of ∫ upper limit x lower limit 0 to take t as the period is that ∫ upper limit t lower limit 0 f (T) DT = 0 (that's it. I don't understand why the definite integral 0 is the algebraic sum of areas. It's hard to find that the definite integral is equal to 0, even if it's any periodic function sequence such as y = SiNx + 5, how can the definite integral be 0?)
(3) Let the continuous function f (x) take t as the period, then all the original functions of F (x) take t as the period if and only if ∫ f (T) DT of upper limit t and lower limit 0 = 0
I didn't get a reward, but I really knelt down to ask for an answer,

First of all, this conclusion can be proved: Let G (x) = ∫ [0 → x] f (T) DT, if G (x) is a function with t as a period, then G (x) = g (x + T) get: ∫ [0 → x] f (t) DT = ∫ [0 → x + T] f (T) DT. Note that the right = ∫ [0 → x] f (T) DT + ∫ [x → x + T] f (T) DT is obtained from (1): ∫ [x → x + T] f (T) DT

Is 1900 a leap year?

On the Gregorian calendar leap year is such a provision: the earth revolves around the sun is called a regression year, a regression year 365 days older 5:48:46 seconds

Calculate the nine palace grid, that is, 1 to 9 to fill in the grid, vertical and oblique add up to 15

This idea can not only solve the problem of adding 3 * 3 lattices, but also solve the problem of odd number lattices such as 5 * 57 * 79 * 9 and so on, and so on. This is the construction method of arbitrary odd order magic square, which was discovered in Dayu's flood control in China as early as that time

Ming and xiao gang went to the mountain where the trees had just been cut down to observe the structure of the stem. They observed that there were many concentric circles in the section of the stem from the inside to the outside. Both of them counted the concentric circles in the cross section of the same tree. Xiao Ming found that there were 17 concentric circles in the bark from the inside to the outside, and Xiao Gang found 20 concentric circles from the inside to the outside
A. This tree may have survived for 17 years. B. this tree may have survived for 37 years. C. This tree may have survived for 20 years. D. this tree must have survived for 17 years

According to the analysis, the formation of the ring is related to the activity of the cambium. Because of the different climate conditions in a year, the cambium is active and weak, which makes the cells formed by it have large and small, and the cell walls are thin and thick

54 7:21 3:15 4:45 10; 45 12:30 8:26 9:24 9:34 11:38

1:54 one fifty-four = six to two 7：21 seven twenty-one = twenty-one past seven 3：15 three fifteen = a quarter past three 4：45 four forty-five = a quarter to five 10:45 ten forty-five = a quarter to...

When using scissors to cut things, it's not easy to cut with the tip of the scissors, but it's easier to cut with the middle of the scissors, because ()
A. Increase the power B. decrease the resistance C. decrease the resistance arm D. increase the power arm

When cutting hard paper with scissors, the size of the resistance arm can be reduced by using the middle part of the knife edge rather than the head part of the knife edge, and the power arm does not change, so it is easy to cut the hard paper; therefore, C

In a cylindrical bottle with a bottom radius of 10 cm, the water depth is 8 cm. To put a piece of iron in the bottle, which is 8 cm in length and 15 cm in width and 15 cm in height, how many cm does the water surface rise when the iron is placed vertically in the water?

3.14 × 102 × 8 ^ (3.14 × 102-8 × 8) - 8, = 2512 ^ 250-8, = 10.048-8, = 2.048 (CM), a: the water surface has risen by 2.048 cm

0 1 3 8 21 () fill in the number according to the rule

The rule is as follows
Three times the number in the middle is equal to the sum of the numbers on both sides
1×3=0+3
3×3=1+8
8×3=3+21
21×3=8+【55】
55 should be filled in brackets

If the definite integral of a continuous periodic function in one period is equal to 0, then there are two roots in any period. Why, When f (x0) is not equal to 0, there must be at least two roots in (x0, x0 + T)