Calculus 12th grade.

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??

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  1. 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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