Final answer:
To find the area of the region between the curve x=ʸ²+y-6, the y-axis, and the lines y=0 and y=3, integrate the curve and evaluate the limits within the given range.
Step-by-step explanation:
To find the area of the region between the curve x=y^2+y-6, the y-axis, and the lines y=0 and y=3, we need to integrate the curve from its intersection point with y=0 to its intersection point with y=3. Since the curve is symmetric about the y-axis, we can find the area in one quadrant and then multiply it by 4 to get the total area. The integral would be:
Area = 4∫[0,3] (ʸ²+y-6) dy
Now we need to find the antiderivative of ʸ²+y-6 with respect to y. After integrating and evaluating the limits, we can calculate the area.