# Integration: the Area Problem - Page 2

Questions

- How do you find the area of the parallelogram with vertices: p(0,0,0), q(-5,0,4), r(-5,1,2), s(-10,1,6)?
- Let R be the region in the first quadrant bounded by the graphs of #(x^2/ 9) + (y^2 /81)=1# and #3x+y=9#, how do you find the area?
- What is the net area between #f(x) = 2x-6 # and the x-axis over #x in [2, 4 ]#?
- How do you find the area of a region using integration?
- How do you find the area inside of the Cardioid #r = 2+2cosθ# and outside the circle r = 3?
- What is the net area between #f(x)=-4x^3+2x^2-5# in #x in[1,5] # and the x-axis?
- What is the net area between #f(x) = cscx -cosxsinx# and the x-axis over #x in [pi/6, (5pi)/8 ]#?
- What is the net area between #f(x) = 2x-5 # and the x-axis over #x in [2, 3 ]#?
- How do you use limits to evaluate #int(x^5+x^2)dx# from [0,2]?
- What is the net area between #f(x) = x^3+6/x # and the x-axis over #x in [2, 4 ]#?
- What is the net area between #f(x) = sqrt(x^2+2x+1) # and the x-axis over #x in [2, 4 ]#?
- Let #R# be the region in the first quadrant bounded by the #x# and #y# axis and the graphs of #f(x) = 9/25 x +b# and #y = f^-1 (x)#. If the area of #R# is 49, then the value of #b#, is ? A) #18/5# B) #22/5# C) #28/5# D) none
- Alex and Veronica were discussing the definite integral #int_0^3 (x^2 − 1)dx#. Alex said it represented the total area bounded by #f(x) = x^2 - 1# and the #x#-axis , between #x = 0# and #x = 3#. Veronica said the total area was larger?
- Let R be the region in the first quadrant bounded above by the graph of #y=(6x+4)^(1/2)# the line #y=2x# and the y axis, how do you find the area of region R?
- How do you find region bounded by circle r = 3cosΘ and the cardioid r = 1 + cosΘ?
- What is the net area between #f(x) = x^2-sqrt(x+1) # and the x-axis over #x in [1, 7 ]#?
- What is the net area between #f(x) = x-sin^2x # and the x-axis over #x in [0, 3pi ]#?
- What is the area under the curve of #x - x^2# in the positive #(x,y)# region?
- What is the net area between #f(x) = 1/sqrt(x+1) # and the x-axis over #x in [1, 4 ]#?
- What is the net area between #f(x) = 2/(x+1)^2 # and the x-axis over #x in [1, 2 ]#?