Integrate ≤ft(x - \;1/x)² with respect to x.

Correct Answer is : x33−2x− 1x+c\;{x³}{3} - 2x - \;1/x + c3x3−2x−x1+c

\;{x³}{3} - x {\;{1}{x³}} + c

\;{x³}{3} - 2x + \;{1}{x³} + c

Correct Answer is : x33−2x− 1x+c\;{x³}{3} - 2x - \;1/x + c3x3−2x−x1+c

Test Index

WAEC Further Mathematics 2014 Paper

Question : 22

Total: 40

Integrate

\left(x - \;\frac{1}{x}\right)^{2}

with respect to x.

Solution:

Concept:

Expand the square first, then integrate term by term using the power rule.

Explanation:

\left(x - \frac{1}{x}\right)^2 = x^2 - 2 + \frac{1}{x^2}

Write

\frac{1}{x^2}

x^{-2}

\int \left(x^2 - 2 + x^{-2}\right) dx

is needed.

Apply the power rule to each term:

\int x^2 \, dx = \frac{x^3}{3}

\int (-2) \, dx = -2x

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

Combine these results and add the constant of integration

c

Answer:

\frac{x^3}{3} - 2x - \frac{1}{x} + c

This matches option D.

Go to Question:

Prev Question

Next Question