SOLUTION: Find the AREA bounded by the graphs of the given equations: 1. {{{ f(x) = x^2 - 6x + 5 }}} and {{{ g(x) = x - 5 }}} 2. {{{ y^2 = x }}} and {{{ x+ 2y = 3 }}}

Algebra ->  Surface-area -> SOLUTION: Find the AREA bounded by the graphs of the given equations: 1. {{{ f(x) = x^2 - 6x + 5 }}} and {{{ g(x) = x - 5 }}} 2. {{{ y^2 = x }}} and {{{ x+ 2y = 3 }}}      Log On


   



Question 1025563: Find the AREA bounded by the graphs of the given equations:
1. +f%28x%29+=+x%5E2+-+6x+%2B+5+ and +g%28x%29+=+x+-+5+
2. +y%5E2+=+x+ and +x%2B+2y+=+3+

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1. +x%5E2+-+6x+%2B+5++=+x+-+5+ ==> x%5E2-7x+%2B+10+=+0 ==> (x-2)(x-5) = 0
==> the two graphs intersect at x = 2, 5.
==> Area is .
The antiderivative is -x%5E3%2F3+%2B+%287x%5E2%29%2F2+-10x.
The area is then .
2. The graphs of +y%5E2+=+x+ and +x%2B+2y+=+3+ intersect at y = -3, 1.
==> Area = int%28%283-2y-y%5E2%29%2C+dy%2C+-3%2C1%29%29.
The antiderivative is 3y+-+y%5E2+-+y%5E3%2F3
==> area is 3%2A1+-+1%5E2+-+1%5E3%2F3+-+%283%2A-3+-+%28-3%29%5E2+-+%28-3%29%5E3%2F3%29+=+32%2F3