Given that dy/dx = {x}, find y.

Correct Answer is : 23x32+c2/3 x³/2} + c32x23+c

Correct Answer is : 23x32+c2/3 x³/2} + c32x23+c

Test Index

WAEC Further Mathematics 2013 Paper

Question : 14

Total: 40

Given that

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

, find y.

Solution:

$\frac{dy}{dx} = \sqrt{x} = x^{\frac{1}{2}}$

$y = \int x^{\frac{1}{2}} \, dx$

= $\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1} + c = \frac{x^{\frac{3}{2}}}{\frac{3}{2}} + c$

= $\frac{2}{3} x^{\frac{3}{2}} + c$

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