# How do you find the area in the first quadrant between the graphs of #y^2=(x^3)/3# and #y^2=3x#?

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To find the area in the first quadrant between the graphs of (y^2 = \frac{x^3}{3}) and (y^2 = 3x), you need to first find the points of intersection between the two graphs by solving the system of equations. Then, integrate the positive difference of the upper and lower curves with respect to (x) from the leftmost intersection point to the rightmost intersection point to find the area. The integral expression for the area is:

[A = \int_{x_1}^{x_2} (y_2 - y_1) , dx]

Where (x_1) and (x_2) are the x-coordinates of the intersection points, and (y_1) and (y_2) are the y-values of the respective curves at a given (x) value.

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