Calculus

Area Between Curves

Area between Curve and x-axis

         

Find the area of the region bounded by yx225y \geq x^2 - 25 and y0y \leq 0.

What is the area of the region bounded by the curve y=9x254xy= 9{x}^2-54x and the xx-axis ?

What is area of the region bounded by the curve y=xy = \sqrt{x} and the xx-axis in the interval 0x4?0 \leq x \leq 4?

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

Let CC be the curve obtained by a parallel translation of the curve y=ax2y=a{x}^2 (a>0)(a>0) by 44 units in the positive direction of the xx-axis. If the area of the region bounded by the curve y=ax2,y=a{x}^2 , the curve C,C, and the xx-axis is 16,16, what is a?a?

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