Given that F¹(x) = x³ √x, find f(x)

Correct Answer is : 2x929{2x^{9/2}}{9}92x29 + c

Correct Answer is : 2x929{2x^{9/2}}{9}92x29 + c

Test Index

WAEC Further Mathematics 2021 Paper

Question : 22

Total: 38

Given that F

^1

^3

√x, find f(x)

Solution:

Concept:

Integration is the reverse process of differentiation. To find the original function, integrate the given derivative.

Explanation:

Given

F'(x) = x^{3}\sqrt{x}

Rewrite using powers:

x^{3}\sqrt{x} = x^{3} \times x^{\frac{1}{2}} = x^{\frac{7}{2}}

Integrate to find

F(x)

F(x) = \int x^{\frac{7}{2}} \, dx

Using the power rule of integration:

F(x) = \frac{x^{\frac{7}{2}+1}}{\frac{7}{2}+1} + c

F(x) = \frac{x^{\frac{9}{2}}}{\frac{9}{2}} + c

F(x) = \frac{2x^{\frac{9}{2}}}{9} + c

Answer:

F(x) = \frac{2x^{\frac{9}{2}}}{9} + c

Correct option: A

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