Question

Find the area between the curve y=1/x and y=1/x+x^2 from x=2 to x=2.

Answer 1

The area between the curves $y=\dfrac{1}{x}$ and $y=x^{2}+\dfrac{1}{x}$ is from x=a to x=b is

$\int_{a}^{b} (x^{2}+\dfrac{1}{x}) dx-\int_{a}^{b}\dfrac{1}{x}dx$ =$\int _{a}^{b} x^{2} dx=[\dfrac{x^{3}}{3}]_{a}^{b}=\dfrac{b^{3}}{3}-\dfrac{a^{3}}{3}$

From x=2 to x=2 the area is clearly zero.