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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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