Can the length formula of any curve be written as ∫ (DX + dy) ^ 1 / 2?

Well, you're missing a DX. The integral sign is a summation sign, but there are infinitely many summation terms. In the future, you will find that there are many formulas for calculating the length of a curve, but they are all evolved from this one. In the future, you will encounter curves expressed by parametric equations, polar coordinates, cylindrical coordinates, and spherical coordinates

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1. ∫ L (x ^ 2 + y ^ 2) DX + (x ^ 2-y ^ 2) dy L is a line segment from a (0,0) to B (1,1) to C (2,0)
2. Z = (1 + x ^ 2 + y ^ 2), then DZ (1,1) is equal to (DX + dy) Such as the title Missed a sign. It should be Z = (1 + x ^ 2 + y ^ 2) open root, then DZ (1,1) is equal to (DX + dy)
3. （2x^2)dy/dx+y=4y^3 The original equation is reduced to (1 / 2x ^ 2) DX = (1 / 4Y ^ 3-y) dy Integral on both sides is - 1 / 6x ^ 3 + C = (1 / 12Y ^ 2-1) ln (4Y ^ 3-y)
4. (SiNx / 1 + x ^ 2) DX f upper limit 1 lower limit - 1 integral! Wrong title is (SiNx / 1 + x ^ 2 + x ^ 4) DX f upper limit 1 lower limit - 1 integral!
5. ∫ 2 π 0|sinx|dx equals () A. 0B. 1C. 2D. 4
6. A ∈ [0, Π / 2], then when ∫ (cosx SiNx) DX (upper limit a, lower limit o) takes the maximum, a=
7. Negative even number, positive odd number, negative odd number are expressed by description
8. For a batch of goods, car a will transport it in 18 hours, car B will transport 1 / 3 of the goods in 8 hours, if car a will transport it in 10 hours first, How many hours will it take for B to transport the rest?
9. 3. If 20 cases of apples are transported by each truck, how many times will the remaining 1080 cases of apples be transported by 3 trucks? (480 cases of apples are transported by 3 trucks in total) will be listed as a comprehensive formula (similar to the off formula calculation)
10. One is a multiple of 8 and the other is a factor of 72. What is this number? What is it
11. For the curve X = y ^ 4-y (a), find dy / DX (b). When the slope is 1 / 3, find the tangent equation
12. Find the slope dy / DX: xy-x = 5 (implicit differential) If you don't understand, I can add a question
13. Zhang's income is 270 yuan. The slope of the indifference curve of store X and Y is dy / DX = - 20 / y. The price of XY is 2 and 5 respectively. How much will Zhang consume X and y?
14. If the slope of a point on the indifference curve dy / DX = - 2, it means that consumers give up a unit of X goods can get () unit of Y goods A、 2 B、 1/2 C、 1/4 D、 4
15. Given the equation X3 + 3xy + Y3 = 0, determine y as the function of X to find dy / DX
16. Ln6y = 3xy, 1) find dy / DX; 2) find d ^ 2Y / DX ^ 2; 3) if d ^ 2Y / DX ^ 2 = 0, the point (x, y) is satisfied
17. The general solution of the first order linear differential equation (x ^ 3 + y ^ 3) dx-3xy ^ 2dy = 0 Such as the title
18. How to find the general solution of equation 3xy ^ 2dy = (y ^ 3-x ^ 2) DX?
19. (x ^ 3 + y ^ 3) dx-3xy ^ 2dy = 0, general solution of homogeneous equation? Answer: x ^ 3-2y ^ 3 = CX
20. General solution for (x ^ 3 + y ^ 3) dx-3xy ^ 2dy = 0