A plane figure D is surrounded by a curve y = e ^ x, a straight line y = e, and a Y-axis. How to find the body of rotation formed by a rotation of plane D around the y-axis

DV = 2 π x (E-E ^ x) DX, x from 0 to 1, v = (E-2) π

RELATED INFORMATIONS

1. Find the volume of the body of revolution formed by a section of arc of hyperbola x ^ 2 / 4-y ^ 2 / 9 = 1 in [2,5] and the plane surrounded by x = 5 rotating around the X axis
2. Find the area of the figure enclosed by the parabola y = x ^ 2 and y = 2x ^ 2, and find the volume of the solid figure formed by the figure rotating around the X axis
3. Find the area of the figure surrounded by X & # 178; + Y & # 178; = 2, X & # 178; + Y & # 178; = 4x, y = x, y = 0
4. As shown in the figure, in the plane rectangular coordinate system, the parabola y = - 1 / 2x & # 178; + 3 / 2x + 2 intersects X axis at two points a and B, and intersects Y axis at point C (1) ABC is a right triangle (2) : the straight line x = m (0 ∠ m ∠ 4) moves on the line ob, intersects the x-axis at point D, intersects the parabola at point E, intersects BC at point F. when m = what, EF = DF? (3) : after connecting CE and be, "is there a point e to maximize the area of triangle BCE?" if there is a point E, calculate the coordinates of point E and the maximum area of triangle BCE
5. It is known that parabola y ^ 2 = 2px (P > 0) and hyperbola x ^ 2 (radical 2-1) ^ 2-y ^ 2 / b ^ 2 = 1 have the same focus F, point a is the focus of two curves, and AF is vertical On the x-axis, the line L and the parabola intersect at two different points c, D If the vector OC * od = m (M is a constant) and the line l only passes through a unique point, the value of M and this point can be obtained
6. Given that the focus F of the parabola y2 = 2px (P > 0) is exactly the right focus of the hyperbola x2a2-y2b2 = 1 (a > 0, b > 0), and the hyperbola passes through the point (3a2p, B2P), then the asymptote equation of the hyperbola is () A. y=±2xB. y=±xC. y=±5xD. y=±153x
7. If the left focus of hyperbola x23 − 16y2p2 = 1 is on the Quasilinear of parabola y2 = 2px, then the value of P is () A. 2B. 3C. 4D. 42
8. Given that the Quasilinear of the parabola y2 = 2px coincides with the left quasilinear of the hyperbola x2-y2 = 2, the focal coordinate of the parabola is______ ．
9. The intersection coordinates of hyperbola y = 8x and straight line y = 2x are______ ．
10. The following propositions are given: proposition 1. The point (1,1) is an intersection of the straight line y = x and the hyperbola y = 1x; Proposition 2. The point (2,4) is an intersection of the straight line y = 2x and the hyperbola y = 8x; proposition 3. The point (3,9) is an intersection of the straight line y = 3x and the hyperbola y = 27x (1) please observe the above proposition and conjecture proposition n (n is a positive integer); (2) use the conjecture of the above question to directly write the solution of inequality 2010x > 20103x
11. The volume of the body of revolution is () A. 8π3B. 10π3C. 6π3D. 32π3
12. The volume of the body of revolution is obtained when the plane figure enclosed by the line y = √ (x-1), x = 4 and y = 0 rotates around the x-axis Review is urgent,
13. Find the volume of the body of revolution formed by the plane figure surrounded by the curve y = x square and x = 3 rotating around the X axis
14. To find the volume of a body of Revolution: a body of revolution formed by a curve (the square of y = x) and a figure surrounded by y = x rotating around the X and Y axes respectively? $(acontent)
15. Use several plane figures to encircle a three-dimensional figure. Plane figures should use at least () plane figures?
16. Xiao Ming wants to encircle the city with iron wire. If he wants to make the triangle area 30 square meters, how long is the iron wire? Just list the equation
17. Find the area of the plane figure surrounded by the following curve X = √ X and the line y = 0, x = 1, x = 2
18. Use three 6.28-meter-long iron wires to encircle the city, rectangular, square and round. Which figure has a large area? Let's make it clear
19. Use 24 cm long wire to circle the learned plane figure. Which figure has the largest area?
20. Use 96cm long wire to encircle a rectangular frame. The ratio of length, width and height of the cuboid is 5:2:3. How many centimeters are the length, width and height of the cuboid