Find an expression for y given that (frac{mathrm d y}{mathrm d x} = x^{2}sqrt{x})
-
A.
(frac{1x^{frac{2}{7}}}{7} + c) -
B.
(frac{2x^{frac{3}{2}}}{7} + c) -
C.
(frac{2x^{frac{7}{2}}}{7} + c) -
D.
(frac{1x^{frac{7}{2}}}{7} + c)
Correct Answer: Option C
Explanation
(x^{2}sqrt{x} equiv x^{2}. x^{frac{1}{2}} = x^{frac{5}{2}})
(implies frac{mathrm d y}{mathrm d x} = x^{frac{5}{2}})
(y = int x^{frac{5}{2}} mathrm d x)
= (frac{x^{frac{5}{2} + 1}}{frac{5}{2} + 1} + c)
= (frac{2x^{frac{7}{2}}}{7} + c)