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## Area Between Curves

In the language of Calculus, the area between two curves is essentially a difference of integrals. The applications of this calculation range from macroeconomic tax models to signal analysis.

# 2 Curves

What is the area of the region bounded by the two curves $y= -{x}^2+2x+13, y= {x}^2 + 9 ?$

If $$m$$ is a positive real number such that the area of the region bounded by the curve $$y={x}^2-x$$ and the line $$y=mx$$ is $$\frac{32}{3},$$ what is $$m?$$

Compute the area bounded by the curve $$y = x^3 - 6x^2 + 9x$$ and the line $$y = x$$.

What is the area of the region bounded by the curves $y= {e}^x - 1, y= 4e^{-x} - 1, y=0?$

What is the area of the region bounded by the curve $$y= -{x}^2+6x$$ and the line $$y=-8x ?$$

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