document.write( "Question 941581: I am trying to find the shaded area (using integration).\r
\n" ); document.write( "\n" ); document.write( "The area is a triangle; no values are given other than 0; (the origin) and the equation listed is x+y=6\r
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Algebra.Com's Answer #574029 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
the graph of y = -x +6 forms a triangle with the x and y axis intersection points, see graph below
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+-x+%2B6%29+\"
\n" ); document.write( "the y axis intercept is (0, 6) and the x axis intercept is (6, 0)
\n" ); document.write( "integral of -x +6 = (-x^2/2) + 6x
\n" ); document.write( "to determine the area under the curve, we evaluate the integral at x = 0 and x = 6
\n" ); document.write( "integral = 0 at x=0
\n" ); document.write( "integral = -18 + 36 = 18 at x = 6
\n" ); document.write( "Area = 18 - 0 = 18
\n" ); document.write( "we can check our answer by using area of triangle formula
\n" ); document.write( "Area = (1/2) * b * h = (1/2) * 6 * 6 = 18
\n" ); document.write( "our answer checks
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