Find an expression for y given that dy/dx = x²{x}

Correct Answer is : 2x727+c{2x^{7/2}}{7} + c72x27+c

Correct Answer is : 2x727+c{2x^{7/2}}{7} + c72x27+c

Test Index

WAEC Further Mathematics 2016 Paper

Question : 30

Total: 40

\frac{dy}{dx} = x^{2}\sqrt{x}

Solution:

$x^{2}\sqrt{x} \equiv x^{2}\cdot x^{\frac{1}{2}} = x^{\frac{5}{2}}$

$\Rightarrow \frac{dy}{dx} = x^{\frac{5}{2}}$

$y = \int x^{\frac{5}{2}} dx$

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

= $\frac{2x^{\frac{7}{2}}}{7} + c$

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