Area Between Two Curves

Find the area between the curves $$y\ =\ x^2$$ and $$y\ =\ 2x$$ from x = 0 to x = 2. Give your answer as a fraction or a decimal to three significant figures.

Determine the area between the curves $$y\ =\ e^x$$ and $$y\ =\ 2e^x$$ from x = 0 to x = 1. Give your answer exactly.

Find the area between $$y\ =\ \sqrt[]{x}$$ and $$y\ =\ x$$ from x = 0 to x = 1. Give your answer as a fraction.

Find the area between $$y\ =\ \sin\ x$$ and $$y\ =\ \cos\ x$$ from x = 0 to $$x\ =\ \frac{\pi}{4}$$

When determining the area between $$y\ =\ x^2$$ and $$y\ =\ 4\ -\ x^2$$ , what would be the bounds (upper and lower limits) on the integral?

Find the area between $$y\ =\ \sqrt[]{x}$$ and $$y\ =\ e^x$$ from x = 0 to x = 1.

Find the area between $$y\ =\ x$$ and $$y\ =\ x^2\ -\ 2$$ from x = -1 to x = 2.

Find the area between $$y\ =\ \sin\ x$$ and $$y\ =\ \cos\ x$$ from x = 0 to x = $$2\pi$$

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