Find an expression for y given that \(\frac{\mathrm d y}{\mathrm d x} = x^{2}\sqrt{x}\)...
FURTHER MATHEMATICS
WAEC 2016
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: C. \(\frac{2x^{\frac{7}{2}}}{7} + c\)
Explanation
\(x^{2}\sqrt{x} \equiv x^{2}. x^{\frac{1}{2}} = x^{\frac{5}{2}}\)
\(\implies \frac{\mathrm d y}{\mathrm d x} = x^{\frac{5}{2}}\)
\(y = \int x^{\frac{5}{2}} \mathrm d x\)
= \(\frac{x^{\frac{5}{2} + 1}}{\frac{5}{2} + 1} + c\)
= \(\frac{2x^{\frac{7}{2}}}{7} + c\)
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