Answer to Question #100026 in Calculus for Francis

Question #100026
1. Find the area bounded by the curve y= x^2+x+4, the x axis from x=1 to x=3.
1
Expert's answer
2019-12-10T11:16:05-0500


The given curve is "y = x^2 + x+ 4"


x is from 1 to 3


Area bounded by the curve and x-axis is A

"= \\int_{x=1}^ {x= 3} y \\space dx"


"= \\int_{x=1}^ {x= 3} (x^2 + x + 4 ) \\space dx"

"= [ \\frac {x^3}{3} + \\frac {x^2} {2} + 4x ]_{x=1} ^{x=3}"

"= \\frac {3^3} {3} + \\frac {3^2}{2} + 4(3) - \\frac {1}{3} - \\frac {1}{2} - 4 (1)"

"= 9 + \\frac {9}{2} +12 - \\frac {1}{3} - \\frac {1}{2} - 4"

"= 17 + \\frac {27-2 -3}{6} = 17 + \\frac {11}{3} = \\frac {62}{3}"

Answer:


Area bounded by the curve and x-axis is "\\frac {62}{3}" .


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