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 \(\frac{1x^{\frac{7}{2}}}{7} + c\)
waec 2016furthermathematics

The correct answer is C. \(\frac{2x^{\frac{7}{2}}}{7} + c\)

\(x^{2}\sqrt{x} \equiv x^{2}. x^{\frac{1}{2}} = x^{\frac{5}{2}}\)

\(\implies \frac{\mathrm d y}{\mathrm d x} = x^{\frac{5}{2}}\)

\(y = \int x^{\frac{5}{2}} \mathrm d x\)

= \(\frac{x^{\frac{5}{2} + 1}}{\frac{5}{2} + 1} + c\)

= \(\frac{2x^{\frac{7}{2}}}{7} + c\)

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