Question on: JAMB Mathematics - 2022
Find the integral of (2x+1)\(^3\)
A
\(\frac{{2x+1}^3}{8}\) + C
B
\(\frac{{2x+1}^4}{8}\) + C
C
\(\frac{{2x+1}^4}{4}\) + C
D
\(\frac{{2x+1}^2}{6}\) + C
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Correct Option: B
To find the integral of (2x+1)^3, we can use the power rule for integration and the chain rule.
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Power Rule: The power rule for integration states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration.
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Apply the rule: In this case, we have ∫(2x+1)^3 dx. Let u = 2x + 1. Then du/dx = 2, which means dx = du/2.
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Substitute and Integrate: Substitute u and dx in the integral: ∫u^3 (du/2) = (1/2)∫u^3 du Applying the power rule:
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