RAM (Rectangle Approximation Method/Riemann Sum) - Page 5

Questions
  • Find the Riemann sum of f(x) = x2-1 on [0,2] by using for subintervals of equal length and midpoint rule?
  • A farmer wants to make a rectangular pasture with 80,000 square feet. If the pasture lies along a river and he fences the remaining three sides, what dimension should he use to minimize the amount of fence needed?
  • Calculate #int_3^7(1/5)x^2dx# using a midpoint Riemann Sum with four increments?
  • Let f=(x/2)+3 be defined on the closed interval {-2,4}, estimate the area under the graph of f above the x-axis using: a. 6 left endpoint rectangles b) 6 right endpoint rectangles?
  • How to use the limit definition (Riemann sum) to evaluate the following integral ?
  • Estimate the area under the graph of f(x) = 2 - sin(x)?
  • Consider the integral given by [a,b]=[0,4]. (a) Find an approximation to this integral by using a Riemann sum with right endpoints and n = 8. Your answer should be correct to four decimal places. R8= ?
  • Find the upper estimate for the total amount of water that leaked out by using five rectangles? Give your answer with one decimal place.
  • How to calculate this? #lim_(x->oo)1/x int_0^xdt/(2+cost)#.
  • Calculate #int(3z^2+2z+1) dz# for #abs z = 1# ?
  • Find the area inside the cardioid given by #r=f(theta)=a(1-costheta)#?
  • Find a closed form expression for the nth right Riemann sum of this integral. HELP!?
  • #int_(Gamma_R) dz/(sin^2 z) =# ?
  • Calculate #lim_(n->oo)sum_(k=1)^n n/(n^2+k^2) =# ?
  • How can I solve the following limit?, I'm trying to solve with Riemann Integral, but I can't get it.
  • Find the Riemann sum of f(x) = sinx on [-p,p]by using four subintervals of equal length and midpoint rule?
  • Estimate (using right endpoints) the given integral?
  • How do I solve this integral? This is the center of gravity of a cone.