Calculating Polar Areas - Page 6

Questions
  • How do you find the area of the region bounded by the spiral #r=7theta# for #0<=theta<=pi#?
  • What is the area cut off the parabola 4y = 3𝑥^2 by the line 2y = 3x + 12 ?
  • The curve with equation #y=x(3-x)^(1/2)# together with line segment OA.!) what are the coordinates of B and A; 2)what is the Area of the shaded region bounded by the line segment AO, x axis and the arc of AB curve?
  • #intint_R(x+y)dA# by circle area is #x^2+y^2=9#?
  • Find the area enclosed by curves y=4x^2 and y=x+3 ?
  • Find the area that is formed by the functions: x=4, y=-1, y=-2 and y=-x?
  • Calculate the area of a small leaf?
  • How do you find areas bounded by polar curves using calculus?
  • A sector of a circle of radius r and angle x=[0,2pi], is to have fixed perimeter P. Find the dimensions r and x that maximize the area (answer given P/4 , 2 radian) ?
  • How to show that of all the rectangles with a given perimeter, the one with greatest area is a square ?
  • Calculus 3 question???? Arc length? calculate the arc length r(t) = (5t sin(t) + 5t cos(t))i + (5t cos(t) - 5 sin(t))j -1< t < 7?
  • What is the distance between the parallel planes #3x + y - 4z = 2# and #3x + y - 4z = 24#?
  • The position of the points A and B, relative to an origin O, are #i-7j# and #4i+kj# respectively, where k is a scalar. The unit vector in the direction of #AB# is #0.6i+0.8j#. What is the value of #k#?
  • Helium is pumped into a spherical balloon at a constant rate of 2 cubic feet per second. How fast is the radius increasing after 4 ​minutes? At what time​ (if any) is the radius increasing at a rate of 140 feet per​ second?
  • What is the area of the parallelogram with vertices at #(0, 1)#, #(1, 0)#, (3, 0)# and #(2, 1)#?
  • Can anyone take a look at the vector problem below?
  • Laplace transforms... How do I go about getting #y#? #y''-2y'-3y=0#, #y(4)=-3#, #y'(4)=-17#
  • Sketch the region enclosed by the given curves and find its area?
  • How do you find the area inside the oval limaçon #r=8+3costheta#?
  • If an isosceles triangle has perimeter P, how long must the legs of the triangle be to maximize its area? (Your answer may depend on P).