Question Type 4: Finding the area between two curves intersection points by finding where the curves intersect and integrating over the region Exercises

Find the area of the region bounded by $y=x^3-x$ and $y=x$.

Determine the area between $y= -x^2 +4$ and $y= x+2$.

Compute the area between the curves $y =\sqrt{x}$ and $y = \frac{x}{2}$ for $x\ge0$.

Find the area enclosed between $y = x^3$ and $y = x$.

Compute the area enclosed by the curves $y=e^x$, $y=x^2$ and the line $x=2$.

Determine the area of the region bounded by the curves $y=\ln x$ and $y=\frac{x}{2}$, and the vertical lines $x=1$ and $x=3.6$.

Find the area enclosed by the curves $y=x^2$ and $y=x^3$.

Calculate the area between $y=x^2$ and $y=2x^2 - x$.

Find the area of the region enclosed by the curves $y = x^2$ and $y = 2x + 3$.

Find the area enclosed by $y=\sin x$ and $y=\cos x$ between $x=0$ and their first positive intersection.

Calculate the area between the curves $y=(x-3)^2$ and $y=4x$.