Friday

July 25, 2014

July 25, 2014

Posted by **Pat** on Friday, October 4, 2013 at 2:28am.

y=x, y=2√x

- Calculus -
**Jai**, Friday, October 4, 2013 at 3:56amReq'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

**Related Questions**

calculus - 1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x...

calculus - 10). Find the area of the region bounded by the graph of f(x)=4lnx/x...

Calculus - Find the area of the region bounded by the line y=3x and y= x^3 + 2x^...

calculus - A region is bounded by the function y=2x^2+3 and the x-axis over the ...

Calculus - 1. Find the area of the region bounded by the curves and lines y=e^x ...

Calculus - Let f be the function given by f(x)=(x^3)/4 - (x^2)/3 - x/2 + 3cosx. ...

calculus - 3). The shaded region is bounded by the y-axis and the graphs of y=1...

calculus - let R be the region bounded by the x-axis, the graph of y=sqrt(x+1), ...

Calculus - find the area of the region described below. f(x)=-4-sq rt of x Find...

Calculus - find the area of the region described below. f(x)= -e^((1/2)x) Find ...