Find ∫(x2 + 3x − 5)dx

Mathematics

JAMB 2017

Find ∫(x² + 3x − 5)dx

A. \(\frac{x_3}{3}\) - \(\frac{3x_2}{2}\) - 5x + k
B. \(\frac{x_3}{3}\) - \(\frac{3x_2}{2}\) + 5x + k
C. \(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) - 5x + k
D. \(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) + 5x + k

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Correct Answer: Option C

Explanation

∫xⁿdx = \(\frac{x_{n + 1}}{n + 1}\)

∫dx = x + k

where k is constant

∫(x² + 3x − 5)dx

∫x² dx + ∫3xdx − ∫5dx

\(\frac{2_{2 + 1}}{2 + 1}\) + \(\frac{3x^{1 + 1}}{1 + 1}\) − 5x + k

\(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) − 5x + k

There is an explanation video available below.

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