Integrate (4x^{-3} - 7x² + 5x - 6) dx.

Correct Answer is : −2x−2−73x3+52x2−6x-2x^{-2} - 7/3x³ + 5/2 x² - 6x−2x−2−37x3+25x2−6x

-2x^{-2} - 7/3x³ + 5/2 x² - 6x

Correct Answer is : −2x−2−73x3+52x2−6x-2x^{-2} - 7/3x³ + 5/2 x² - 6x−2x−2−37x3+25x2−6x

Test Index

JAMB Mathematics 2019 Paper

Question : 58

Total: 73

Integrate

\int (4x^{-3} - 7x^2 + 5x - 6) dx

Solution:

Concept:

Use the power rule for integration:

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

for

n \neq -1

Explanation:

Integrate each term of the polynomial separately.

\int 4x^{-3} \, dx = \frac{4x^{-2}}{-2} = -2x^{-2}

\int -7x^2 \, dx = -\frac{7x^{3}}{3} = -\frac{7}{3}x^3

\int 5x \, dx = \frac{5x^{2}}{2}

\int -6 \, dx = -6x

Combine all the integrated terms.

\int (4x^{-3} - 7x^2 + 5x - 6) \, dx = -2x^{-2} - \frac{7}{3}x^3 + \frac{5}{2}x^2 - 6x + C

Answer:

-2x^{-2} - \frac{7}{3}x^3 + \frac{5}{2}x^2 - 6x + C

This matches option A.

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