What does the mathematical symbol "∮" mean?

Loop integration means integrating a closed curve

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4. [(12.56/3.14)^2*3.14/(4*3)]/(1^2*3.14)=1.3m ^
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6. How can we get the result of ∫ (upper Π / 4 lower 0) tanxdx = lncosx I (upper Π / 4 lower 0)?
7. Given that the derivative of the function f (x) = AX3 + bx2 + CX is even, then A f (x) is an even function B F (x) is an odd function C f (x) has both maxima and minima
8. Let the minimum value of F (x) = ax ^ 3 + BX ^ 2 + CX be - 8, and the image whose derivative y = f '(x) passes through the point (- 2,0) (2 / 3,0), The minimum value of F (x) is - 8. Can (- 8,0) be brought in? Isn't the minimum a point with zero derivative?
9. Let the minimum value of F (x) = ax ^ 3 + BX ^ 2 + CX be - 8, and the image of its derivative function y = f '(x) passes through the point (- 2,0) (2 / 3,0) My equation is 64x3a-16b + C = 0 -8a+4b-2c=0 (8 / 27) a + (4 / 9) B + (2 / 3) C = 0, how to solve these three equations and find the process B = - C and what happened? Everybody speed... T-T
10. Let the minimum value of F (x) = ax ^ 3 + BX ^ 2 + CX be - 8, and the image of its derivative function y = f '(x) passes through points (- 2,0) and (2 / / 3,0), as shown in the figure (1) Finding the analytic expression of F (x) (2) If f (x) ≥ m ^ 2-14m holds for X ∈ [- 3,3], the value range of real number m is obtained (the picture shows: the opening of the image is downward, the intersection of the image and the X axis is - 2,2 / 3, and the intersection of the image and the Y axis is above.)
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12. (ln1/3+ln1+ln3+ln9+… +ln729)log3^e
13. About how mathematics compares the sizes of ln1-2 and ln3-1, Can LNX images be drawn
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15. ln3-ln1=?ln2-ln0.5=?
16. ln3÷ln1/3
17. A = LN2 / 2, B = Ln3 / 3, C = LN5 / 5, then what is the size of the three and why?
18. It is known that a = ln 3 / 3, B = LN 2 / 2, C = ln 5 / 5 A = (LN2) / 2 = ln (radical 2), B = (Ln3) / 3 = ln (root 3 of degree 3), C = (LN5) / 5 = ln (quintic root 5) Root 5 < root 2 < root 3 So: C
19. A = LN2 / 2, B = Ln3 / 3, C = LN5 / 5, then the size relationship of a, B, C is
20. If a = (LN2) / 2, B = (Ln3) / 3, C = (LN5) / 5. What are the sizes of a, B, C