Linda M.
asked • 02/14/22Determine the area of the region enclosed
Determine the area of the region enclosed by y=√x+3, x=−3, and y=4. Round your limits of integration and answer to 2 decimal places.The area of the encloses a region is square units.
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1 Expert Answer
Region is made up of a rectangle from x=-3 to 0 and y from 0 to 4, plus it has a figure between y = sqrt(x) + 3 and y=4 where x goes from 0 to the intersection of both curves. Find intersection by setting sqrt(x) + 3 = 4 and solve for x. x will equal 1. Then integrate 4 - (sqrt(x) + 3) from 0 to 1. This antiderivative will equal x - 2/3(x3/2). Evaluate at end points. You will get an area of 1/3. Add this to area of rectangle which is 12. Total area will equal 37/3.
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Doug C.
sqrt(x+3) or sqrt(x)+3? The fact that you are asked to round the limits of integration seems to suggest the latter.02/14/22