Integrate the expression 6x² - 2x + 1

Correct Answer is : 2x3³3 - x2²2 + x + c

Correct Answer is : 2x3³3 - x2²2 + x + c

Test Index

JAMB Mathematics 2018 Paper

Question : 32

Total: 62

^{2}

- 2x + 1

Solution:

Concept:

Integration is the reverse of differentiation. Apply the power rule:

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

Explanation:

Integrate each term of

6x^{2} - 2x + 1

separately.

For

6x^{2}

\int 6x^{2} \, dx = 6 \cdot \frac{x^{2+1}}{2+1} = \frac{6x^{3}}{3} = 2x^{3}

For

-2x

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

For

1

\int 1 \, dx = x

Combine the results and add the constant of integration

c

Thus,

\int (6x^{2} - 2x + 1) \, dx = 2x^{3} - x^{2} + x + c

Answer:

2x^{3} - x^{2} + x + c

(Option B).

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