검증된 단계별 안내
06:21
05:43
05:3652–54. Force on a window A diving pool that is 4 m deep and full of water has a viewing window on one of its vertical walls. Find the force on the following windows.
The window is circular, with a radius of 0.5 m, tangent to the bottom of the pool.
Find the area of the region described in the following exercises.
The region in the first quadrant bounded by y=x^2/3 and y=4
Assume f and g are continuous, with f(x) ≥ g(x) ≥ 0 on [a, b]. The region bounded by the graphs of f and g and the lines x=a and x=b is revolved about the y-axis. Write the integral given by the shell method that equals the volume of the resulting solid.
39–44. Shell method about other lines Let R be the region bounded by y = x²,x=1, and y=0. Use the shell method to find the volume of the solid generated when R is revolved about the following lines.
x =2
Suppose f and g have continuous derivatives on an interval [a, b]. Prove that if f(a)=g(a) and f(b)=g(b), then ∫a^b f′(x) dx = ∫a^b g′(x) dx.
Let f(x) = {x if 0≤x≤2
2x−2 if 2<x≤5
−2x+18 if 5<x≤6.
Find the volume of the solid formed when the region bounded by the graph of f, the x-axis, and the line x=6 is revolved about the x-axis.
