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:

Concept:

Integrate the given derivative to recover the original function

y

Explanation:

We are given

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

Rewrite the square root in index form:

\sqrt{x} = x^{\frac{1}{2}}

To find

y

, integrate both sides with respect to

x

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

Use the power rule for integration:

\int x^n \, dx = \frac{x^{n+1}}{n+1} + c

Here

n = \frac{1}{2}

, so:

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

Simplify the fraction:

\frac{1}{\frac{3}{2}} = \frac{2}{3}

Therefore,

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

Answer:

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

Correct option: B.

Go to Question:

Prev Question

Next Question