The formula to use in finding the surface area of the revolved curve is {eq}\displaystyle S=2\pi \int_{a}^{b}y\sqrt{1+\left ( f'(x) \right )^{2}}dx {/eq} where {eq}\displaystyle \int_{a}^{b}\sqrt{1+\left ( f'(x...
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...
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...
Find the area of the surface obtained by rotating the curve y=2−x2;0≤x≤4 about the y-axis. Area of a rotated surface: Integration is used to find area of surface rotated around an axis. Let f be a function on [a,b] then take...
Various strain amplitudes can be attained by altering the wire diameter and the radius of the curvature. Alternating strains are then applied by rotating the curved wire about its longitudinal axis as presented in Fig. 2. For the rotating-bending test setup shown in Fig. 2(a), the wire is...
White dwarfs, the extremely dense remnants left behind by most stars after their death, are characterized by a mass comparable to that of the Sun compressed into the size of an Earth-like planet. In the resulting strong gravity, heavy elements sink towar
The rotating anode (24) is formed from a section of a sphere. It can be made to tilt about a pivoting point (28) by a motor (26) and a spindle (27). The pivot is located at the centre of curvature of the surface of the anode (24). It also lies on the axis of rotation (...
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....
The action is S= √ −gd 4 x R 16π G + Lm (1) where the first term represents Einstein gravity, the second term Lm is marked as the matter Lagrangian about an axion field and a scalar field, and defined as follows Lm = −∇μ ψa∗ ∇ μψa − Ua(|ψa|2) −...
Find the exact area of the surface obtained by rotating the curve about the x-axis. y=(7−x), 1≤x≤7Surface Area:The surface area of a three-dimensional shape is the quantity surrounding it on all sides. To calculate an object's total ...