The volume of the geometry obtained by rotating the curve y = X2 (0 ≤ y ≤ 1) around the Y axis

The volume of geometry obtained by rotating the curve y = x & # 178; (0 ≤ y ≤ 1) around the y-axis
Volume v = [0,1] ∫ π X & # 178; dy = [0,1] π∫ YDY = π (Y & # 178 / 2) [0,1] = (1 / 2) π

RELATED INFORMATIONS

1. Find the area a of the figure enclosed by the curve y = e ^ x, y = 2 and x = 0, and the volume of one revolution around the Y axis Using the knowledge of definite integral,
2. The area of the figure enclosed by the curve y = x & # 178; - 1 and X axis is equal to
3. The area of the figure enclosed by the curve expressed by the equation | x | + | y | = 1 is () A. 2B. 2C. 1D. 4
4. Let a + B + C = 1 vector OP = a vector OA + B vector ob + C vector OC, how can we prove that p a B C four points are coplanar?
5. As shown in the figure, it is known that in isosceles △ ABC, ab = AC, P and Q are points on edge AC and ab respectively, and AP = PQ = QB = BC=______ ．
6. If there is a common point between the line L passing through point a (4,0) and the curve (X-2) 2 + y2 = 1, the range of the slope of the line L is () A. [−3，3]B. (−3，3)C. [−33，33]D. (−33，33)
7. If the circle x2 + y2 = 4, a (- 1,0) and B (1,0) move the parabola through two points a and B, and the tangent of the circle is taken as the guide line, then the focus trajectory equation of the parabola is () A. x25+y23＝1(y≠0)B. x24+y23＝1(y≠0)C. x25+y24＝1(y≠0)D. x23+y24＝1(y≠0)
8. When t belongs to R, the graph represented by parameter equation x = (- 8t) / (4 + T ^ 2), y = (4-T ^ 2) / (4 + T ^ 2) is____
9. In the plane rectangular coordinate system, the coordinates of the end point of the line AB are a (- 2,4), B (4,2), and the line y = kx-2 always has an intersection with the line. The value range of K is calculated After taking the endpoint coordinates in, we can calculate k = 1 and K = - 3. Why should it be greater than or equal to 1 and less than or equal to - 3
10. 1. Draw a secant from a point outside the circle P (1,1) to the circle x2 + y2 = 1, intersect the circle at two points a and B, and find the trajectory equation of the midpoint of the chord ab
11. Given that the vertex of the parabola is (- 1,4), and the length of the line segment cut on the x-axis is 6, the analytical formula of the parabola is obtained
12. As shown in the figure, it is a part of the image of an inverse scale function, and points a (1,10) and B (10,1) are its endpoints. (1) find the analytic expression of the function, and write out the value range of the independent variable x; (2) please give an example of life that can be described by the functional relationship of this problem
13. As shown in the figure, it is known that the two vertices of RT △ OAB are a [6,0], B [0,8], O is the origin, and △ OAB rotates 90 ° clockwise around point A. point O arrives at point o ', and point B arrives at point B' (1) Finding the coordinates of point B 丿 (2) Finding the analytic expression of the function corresponding to the line ab 丿
14. It is known that the ordinate of an intersection of the inverse scale function y = KX and the linear function y = 2x + k is - 4, then the value of K is -___ ．
15. If there is an intersection point between the image of inverse scale function y = 2 / X and the image of primary function y = kx-4, the value range of K is obtained Hope as soon as possible
16. If the inverse scale function y = K / X intersects with the image of the first-order function y = KX + 2, then the value range of K is Such as the title
17. As shown in the figure, the image of the first-order function y = KX + 2 and the inverse scale function y = K / X intersects a (4, m)
18. It is known that the intersection point of the image with the inverse scale function y = K / X and the linear function y = MX + n is a3,4 And the distance from the intersection of the image of the first-order function and the x-axis to the origin is 5 Finding two analytic expressions Find the coordinates of another point and determine what type of angle AOB is
19. If the image of a function of degree passes through points (3,5) and (- 4, - 9), then the coordinates of the intersection of the image of the function and the y-axis are______ ．
20. If the image of a function of degree passes through points (3,5) and (- 4, - 9), then the coordinates of the intersection of the image of the function and the y-axis are______ ．