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
b. 8 1/3
c. 10 2/3
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~ :)
Answer This Question
More Related Questions
- Calculus - Find the exact area below the curve y=x^3(4-x)and above the x-axis
- Calculus - Find the exact area below the curve (1-x)*x^9 and above the x axis
- 12th grade calculus - find points on the curve x^2+xy+y^2=7 (a) where the tangen...
- Calculus - Find the dimensions of the rectangle of largest area that has its ...
- 12th grade calculus - How do I find the area bounded by the curver y = x^1/2 + 2...
- 12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...
- calculus - Find area of the region under the curve y = 5 x^3 - 9 and above the x...
- Calculus - Find the area cut off by x+y=3 from xy=2. I have proceeded as under: ...
- calculus - Find the volume of the solid generated by revolving the region about ...
- calculus - find the volume of the solid of revolution obtained by revolving the ...