Find ∫(x 2 + 3x − 5)dx

Correct Answer is : x33x₃/33x3 + 3x223x₂/223x2 - 5x + k

Correct Answer is : x33x₃/33x3 + 3x223x₂/223x2 - 5x + k

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JAMB Mathematics 2017 Paper

Question : 34

Total: 44

Find ∫(x² + 3x − 5)dx

Solution:

Concept:

Use the power rule of integration:

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

for each term.

Explanation:

Write the integral as the sum of separate integrals:

\int (x^2 + 3x - 5)dx = \int x^2 dx + \int 3x dx - \int 5 dx

Apply the power rule to each term.

For

x^2

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

For

3x

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

For

-5

\int 5 dx = 5x

Combine the results and add the constant of integration

k

\frac{x^{3}}{3} + \frac{3x^{2}}{2} - 5x + k

Answer:

\frac{x^{3}}{3} + \frac{3x^{2}}{2} - 5x + k

This matches option C.

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