aA surface of revolution is generated by rotating the curve about the -axis. Find the unit normal vector at the point to the surface that points outwards 革命表面是通过转动曲线引起的 关于-轴。 发现单位正常传染媒介在点对表面那点向外[translate]...
The surface area of rotation of a curve y=f(x) about x-axis is s=∫2πyds where ds=1+(dydx)2dx, a≤x≤b. If the curve is x=h(y),c≤y≤d and it is rotated about y-axis, then the surface area of solid of revolution is s=∫2...
We will use the following formula to find the surface area of revolution of of the given curve about the x-axis: {eq}\displaystyle A=2\pi \int_{x_1}^{x_2}y \sqrt{1+\left(\frac{dy}{dx}\right)^2} \, dx\\ {/eq} So, we will find...
Answer to: Calculate the exact area of the surface obtained by rotating the curve about the x-axis. x = 2 + 3y^2, 1 less than or equal to y less...
A solid is formed by rotating the region bounded by the curve y = c and the r-axis between r = 0 and r = 1. around the r-axis. It was shown in Example I on page 399 that the volume of this solid is x(1-r-2)/2.Assuming the solid has constant density d. find I and g....
aIn mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line (the axis) 在数学,工程学和制造,革命固体是转动得到的一个立体图形一条平面曲线在某一直线附近 (轴) [translate] ...
Figure 15-4 shows a three-bladed propeller rotating about an axis of rotation. The spinner is an aerodynamically shaped cover that (1) reduces the drag of the hub of the propeller and (2) protects it from the elements. The pressure differential between the front and aft face of the prope...
1 Introduction It has been shown that a mysterious entity known as dark energy is speeding up the expansion of our universe. As its composition cannot be determined by sight, dark energy might be made of any material. One of the things that might be thought of as a dark-energy model is...
Answer to: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = (1/3)(y^2 + 2)^(3/2), 2 less than or equal to y...
Find the exact area of the surface obtained by rotating the curve about the x-axis: {eq}f(x)=2 {/eq} {eq}\sqrt x \ where \ \ 1 \leq x \leq 3 {/eq} Surface area The curve f(x) is rotated about {eq}\displaystyle x- ...