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Evaluate the area of a region bounded by y=sqrt x, y=3, and y axis.

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Final answer:

To evaluate the area of the region bounded by y=sqrt x, y=3, and y axis, we need to find the points of intersection between these curves and integrate the function sqrt(x) from x = 0 to x = 9.

Step-by-step explanation:

To evaluate the area of the region bounded by the curves y = sqrt(x), y = 3, and the y-axis, we need to find the points of intersection between these curves. Setting the equations equal to each other, we get:

sqrt(x) = 3

Squaring both sides, we have:

x = 9

So, the region is bounded by x = 0, x = 9, and y = 3. The area can be calculated by integrating the function sqrt(x) from x = 0 to x = 9:

Area = ∫(0 to 9) sqrt(x) dx

Using the power rule of integration and evaluating the integral, we find that the area of the region is 18 square units.

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