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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.

# Area between Curve and x-axis

Find the area of the region bounded by $$y \geq x^2 - 25$$ and $$y \leq 0$$.

What is the area of the region bounded by the curve $$y= 9{x}^2-54x$$ and the $$x$$-axis ?

What is area of the region bounded by the curve $$y = \sqrt{x}$$ and the $$x$$-axis in the interval $$0 \leq x \leq 4?$$

ParallelAngleBisector

Consider the region bounded by the curve $$f(x)= x(x-b)(x-a)$$ and the $$x$$-axis, where $$b=5$$ and $$a > 5$$. If the bounded region above the $$x$$-axis and the bounded region below the $$x$$-axis have the same area, what is the value of $$a ?$$

Let $$C$$ be the curve obtained by a parallel translation of the curve $$y=a{x}^2$$ $$(a>0)$$ by $$4$$ units in the positive direction of the $$x$$-axis. If the area of the region bounded by the curve $$y=a{x}^2 ,$$ the curve $$C,$$ and the $$x$$-axis is $$16,$$ what is $$a?$$

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