Posted by Pat on Friday, October 4, 2013 at 2:28am.
Find the area of the region bounded by the graphs of the given equations:
y=x, y=2√x

Calculus  Jai, Friday, October 4, 2013 at 3:56am
Req'd: area bounded by y = x and y = 2*sqrt(x)
First thing to do here is to find their points of intersection, so we'll know the bounds. We can do it algebraically or graphically.
To find algebraically the points of intersection, we just use substitution. Since y = x,
y = 2*sqrt(x)
x = 2*sqrt(x)
x^2 = 4x
x(x  4) = 0
x = 0 and x = 4
To set up the integral, we choose whether vertical strips (dx) or horizontal strips (dy) to be used. In here, let's just use vertical (dx). The bounds for this is from x = 0 to x = 4, and since it is dx, all expressions must be in terms of x.
Therefore,
Integral (2*sqrt(x)  x)dx from 0 to 4
= (2*(2/3)*(x^3/2)  (1/2)x^2) from 0 to 4
= ((4/3)x^3/2  (1/2)x^2) from 0 to 4
= [ ((4/3)(4^(3/2))  (1/2)*4^2 ]  [ ((4/3)(0^(3/2))  (1/2)*0^2 ]
= (4/3)(8)  (1/2)(16)  0
= 32/3  8
= 32/3  24/3
= 8/3 square units
Hope this helps~ :3
Answer This Question
Related Questions
 Calculus  How do I find the area of the region bounded by the graphs of the ...
 calculus  1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x...
 calculus  3). The shaded region is bounded by the yaxis and the graphs of y=1...
 calculus  find the area the region bounded by the graphs of the given equation ...
 calculus  set up sums of integrals that can be used to find the area of the ...
 Calculus Voulme  find the volume of the solid generated by revolving the region...
 Calculus  1. Find the area of the region bounded by the curves and lines y=e^x ...
 Calculus  "Find the volume of the solid generated by revolving the region ...
 calculus  Sketch the region bounded by the graphs of the algebraic functions & ...
 calculus  FInd the area of the region bounded by the graphs of y= 3x^2+1 , y=0...
More Related Questions