Answer to Question #340673 in Calculus for Jane

Question #340673

Find the area, take the elements of the area perpendicular to the x-axis. x²-y+1=0; x-y+1=0.

1
Expert's answer
2022-05-15T23:10:55-0400
"x^2-y+1=0=>y=x^2+1"

"x-y+1=0=>y=x+1"

"x^2+1=x+1"

"x^2=x"

"x_1=0, x_2=1"

"Area=A=\\displaystyle\\int_{0}^{1}(x+1-(x^2+1))dx"

"=\\displaystyle\\int_{0}^{1}(x-x^2)dx=[\\dfrac{x^2}{2}-\\dfrac{x^3}{3}]\\begin{matrix}\n 1 \\\\\n 0\n\\end{matrix}=\\dfrac{1}{6}({unis}^2)"

Area is "\\dfrac{1}{6}" square units.



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