Find the area bounded by the curve y = x 1/2 + 2, the x-axis, and the lines x = 1 and x = 4 A. 16 B. 10 2/3 C. 7 1/2 D. 28 1/2

To find the area of the curve subject to these constraints, we must take the integral of y = x ^ (1/2) + 2 from x=1 to x=4

Take the antiderivative: Remember that this what the original function would be if our derivative was x^ (1/2) + 2

antiderivative (x ^ (1/2) + 2) = (2/3) x^ (3/2) + 2x

* To check that this is correct, take the derivative of our anti-derivative and make sure it equals x^ (1/2) + 2

To find integral from 1 to 4:

Find anti-derivative at x=4, and subtract from the anti-derivative at x=1

2/3 * 4 ^ (3/2) + 2 (4) - (2/3) * 1 - 2*1

2/3 (8) + 8 - 2/3 - 2 Collect like terms

2/3 (7) + 6 Express 6 in terms of 2/3

2/3 (7) + 2/3 (9)

2/3 (16) = 32/3 = 10 2/3 Answer is B