Questions asked by Napoléon Bonaparte

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• How do you evaluate #int (x^3 + 2x^2 + 5x - 2)/(x^2 + 2x + 2)^2 dx#?
  
• Which of the following integrals can be best evaluated using integration by parts?
  
• How do you evaluate #int_0^1# #sqrt(x - x^2)# dx?
  
• How do you evaluate #int# #arctan(sqrt(x))/sqrt(x)# dx?
  
• How do I find out which rule produced which estimate and the two approximations that the true value of #int_0^2# f(x) dx lie in?
  
• Which of the following are improper integrals?
  
• How do you evaluate #int# s #3^s# ds?
  
• How do you evaluate sqrt(64 + x^2)/x?
  
• How do you evaluate #int# #sqrt(x^2 + 14x)# dx?
  
• How do you evaluate #int# #dx/(x^2sqrt(x^2 - 9))# with x = 3sec(#theta#)?
  
• What can you say about the graph of a solution of the equation y' = #(xy^3)/36# when x is close to 0?
  
• How do you find the moments #M_x# and #M_y# and the center of mass of the system?
  
• How do you solve the differential equation #dy/dx = 7x sqrt(y)#?
  
• For what values of r does the function y = #e^(rx)# satisfy the differential equation 5y'' + 14y' − 3y = 0?
  
• What should I put for using the integral test to determine whether the series is convergent or divergent?
  
• Does sodium bicarbonate become heavier when heated above 500 degrees Celsius?
  
• Are all polyatomic ions ionic?
  
• Suppose that 6 J of work is needed to stretch a spring from its natural length of 34 cm to a length of 49 cm. How do you answer (a) and (b)?
  
• A triangular plate with height 6 ft and a base of 8 ft is submerged vertically in water so that the top is 3 ft below the surface. How do you express the hydrostatic force against one side of the plate as an integral and evaluate it?
  
• The differential equation below models the temperature of a 95°C cup of coffee in a 21°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 71°C. How to solve the differential equation?