Posted by anon on Saturday, March 5, 2011 at 9:44pm.
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~ :)
Related Questions
Calculus - Find the exact area below the curve (1-x)*x^9 and above the x axis
Calculus - Find the dimensions of the rectangle of largest area that has its ...
Calculus - The graph of the curve y2=10 x+10 is a parabola, symmetric with ...
calculus - Find area of the region under the curve y = 5 x^3 - 9 and above the x...
Math - 1. The curve y=10/2x+1 -2 intersects the x-axis at A. The tangent to the ...
12th grade calculus - How do I find the area bounded by the curver y = x^1/2 + 2...
calculus - find the volume of the solid of revolution obtained by revolving the ...
calculus - find the volume of the solid of revolution obtained by revolving the ...
12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...
calculus - The region A is bounded by the curve y=x^2-5x+6 and the line y = -x...
For Further Reading
