Given that (frac{mathrm d y}{mathrm d x} = sqrt{x}), find y.
-
A.
(2x^{frac{3}{2}} + c) -
B.
(frac{2}{3}x^{frac{3}{2}} + c) -
C.
(frac{3}{2}x^{frac{3}{2}} + c) -
D.
(frac{2}{3}x^{2} + c)
Correct Answer: Option B
Explanation
(frac{mathrm d y}{mathrm d x} = sqrt{x} = x^{frac{1}{2}})
(y = int x^{frac{1}{2}} mathrm {d} x)
= (frac{x^{frac{1}{2} + 1}}{frac{1}{2} + 1} + c = frac{x^{frac{3}{2}}}{frac{3}{2}} + c )
= (frac{2}{3}x^{frac{3}{2}} + c)