Calculus

Area Between Curves

Area between Curve and y-axis

         

If the blue curve in the above diagram represents the graph of x=y3300yx={y}^3-300y and the vertical lines are tangent lines to the curve, what is the area of the shaded region?

What is the area of the region bounded by the curve x=y2+100x= -{y}^2+100 and the yy-axis ?

Let SS be the area bounded by y2xy^2 \leq x, x25x \leq 25 and y0y \geq 0. If S=abS = \frac{a}{b}, where aa and bb are coprime positive integers, what is the value of a+ba+b?

What is the area of the region bounded by the curve x=6y(y4)x= -6y(y-4) and the yy-axis ?

If g(x)g(x) is the inverse function of f(x)=10cosxf(x)=10\cos x (0xπ2),(0 \leq x \leq \frac{\pi}{2}) , what is the area of the region bounded by y=g(x),y=g(x) , the xx-axis and yy-axis?

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