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
x2y+1=0=>y=x2+1x^2-y+1=0=>y=x^2+1

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

x2+1=x+1x^2+1=x+1

x2=xx^2=x

x1=0,x2=1x_1=0, x_2=1

Area=A=01(x+1(x2+1))dxArea=A=\displaystyle\int_{0}^{1}(x+1-(x^2+1))dx

=01(xx2)dx=[x22x33]10=16(unis2)=\displaystyle\int_{0}^{1}(x-x^2)dx=[\dfrac{x^2}{2}-\dfrac{x^3}{3}]\begin{matrix} 1 \\ 0 \end{matrix}=\dfrac{1}{6}({unis}^2)

Area is 16\dfrac{1}{6} square units.



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