Posted by **anon** on Saturday, March 5, 2011 at 9:44pm.

Find the area lying above the x axis and below the parabolic curve y= 4x -x^2

a.8

b. 8 1/3

c. 10 2/3

d. 16

B or C not sure??

- Calculus 12th grade. -
**jai**, Saturday, March 5, 2011 at 10:21pm
first, we find where the curve touches the x-axis, or simply get the roots,, to get the roots, equate y = 0:

0 = 4x - x^2

0 = x(4-x)

x = 0 and x = 4

this will be our boundary conditions for integration,, we'll use integration since area under the curve:

integral (4x - x^2) = 2x^2 - (1/3)X^3

at x = 0, the integral becomes

2*0^2 - (1/3)*0^3 = 0

at x = 4 the integral becomes

2*(4^2) - (1/3)*4^3

32 - 64/3

96/3 - 64/3

32/3 = 10 2/3

thus integral from 0 to 4 = 10 2/3 - 0 = 10 2/3

hope this helps~ :)

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