Integral ∫(5x³ + 7x² - 2x + 5)dx

Correct Answer is : 5x44+7x33−x2+5x+C5x^4/4 + 7x³/3 - x² + 5x + C45x4+37x3−x2+5x+C

Correct Answer is : 5x44+7x33−x2+5x+C5x^4/4 + 7x³/3 - x² + 5x + C45x4+37x3−x2+5x+C

Test Index

JAMB Mathematics 2015 Paper

Question : 43

Total: 61

Integral ∫

(5x^3 + 7x^2 - 2x + 5)

Solution:

Concept:

Integrate each term of the polynomial separately using the power rule

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

Explanation:

Apply the power rule to each term in the integrand:

\int 5x^3\,dx = \frac{5x^{4}}{4}

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

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

\int 5\,dx = 5x

Add the constant of integration

C

Therefore, the integral is:

\frac{5x^{4}}{4} + \frac{7x^{3}}{3} - x^{2} + 5x + C

Answer:

The correct option is B:

\frac{5x^{4}}{4} + \frac{7x^{3}}{3} - x^{2} + 5x + C

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