Calculate the first curvilinear integral ∫ xyds, where C is the entire boundary of a triangle with curved edges bounded by y equal to x square, y = 0 and x = 1

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• 1. The range of surface integral ∫ (a ^ 2 + x ^ 2 + y ^ 2) ^ 0.5 DS is the upper part of sphere x ^ 2 + y ^ 2 + Z ^ 2 = a ^ 2
• 2. Let ∑ be a sphere x ^ 2 + y ^ 2 + Z ^ 2 = 4, then the curved area is divided into ∮ (x ^ 2 + y ^ 2 + Z ^ 2) ds=
• 3. I = FF (x ^ 2 + y ^ 2) ds, where the surface is spherical x ^ 2 + y ^ 2 + Z ^ 2 = 2 (x + y + Z)
• 4. Find the curve integral ∫ L (x + y) ds, l is the straight line segment connecting (1.0) (0.1) two points. (PS: explain how DS is transformed into DX)
• 5. Let l be a line segment from a (1,0) to B (- 1,2), then the curve integral ∫ L (x + y) ds
• 6. It is known that the absolute value of x = 4, the absolute value of y = 1 / 2, and XY is less than 0, the absolute value of X of y of the ball The writing process is the best
• 7. As shown in the figure, the straight line y = 2x moves 2 units along the positive direction of x-axis, intersects with X-axis at point a, and intersects with hyperbola y = 6 / X and hyperbola y = K / X at two points BC respectively, And the area of triangle OBC = the area of triangle OAB, K=
• 8. If you translate the straight line y = - 2x + 6 downward by how many units, you can get that there is only one intersection point between the new straight line and the hyperbola y = 1 / x?
• 9. High number: l is the circle x square + y square; find L (x square + y Square) ds under ∮
• 10. High number LIM (x - > 0) TaNx / x ^ 3-x ^ 2-2x why TaNx ~ x ^ 3-x ^ 2-2x ~ (- 2x)
• 11. Calculate the curve integral ∮ (x ^ 2 + y ^ 2) ds C as x = acost, y = asint (0
• 12. Point a moves in a circle with the origin as the center of the circle at a uniform speed in a counter clockwise direction. It is known that point a starts from the positive half axis of x-axis, turns the angle of θ (0 ＜ θ ＜ π) in one minute, reaches the third quadrant in two minutes, and returns to the original position in 14 minutes, then θ=______ ．
• 13. A point a on the circle moves in a circle at a constant speed in a counter clockwise direction Known point a turns angle a every minute (0 〈 a 〈 Wu), reaches the third quadrant after 2 minutes, returns to the original position after 14 minutes, and calculates the size of A
• 14. Point a moves in a circle with the origin as the center of the circle at a uniform speed in a counter clockwise direction. Given that point a starts from the positive half axis of x-axis and turns angle a (0 ＜ a ＜ 180) for 1min, reaches the third quadrant for 2min, and returns to the original position for 14min, then a =?
• 15. A point a on the circle moves in a circular motion with uniform velocity in a counter clockwise direction For example, the known point a turns angle a every minute (0 〈 a 〈 Wu), reaches the third quadrant after 2 minutes, returns to the original position after 14 minutes, and calculates the size of A
• 16. A necessary and sufficient condition for the curve of equation (x-a) ^ + (y-b) ^ = R ^ to pass through the origin
• 17. A necessary and sufficient condition for the curve of equation (x-a) * 2 + (y-b) * 2 = R * 2 to pass through the origin
• 18. When a, B and C satisfy what conditions, the curve of equation (x-a) ^ 2 + (y-b) ^ 2 = R ^ 2 passes through the origin When a, B and C satisfy what conditions, the curve of equation y = ax ^ 2 + BX + C passes through the origin
• 19. The distance from the moving point m to the fixed point a (- 3,0) is two times of the distance to the origin. The trajectory of the moving point m is a curve C. The equation of the curve C is obtained
• 20. The curve xy = - 1 is obtained by rotating 45 ° anticlockwise around the coordinate origin