Evaluate ∫(2x+3)12δx

Assessment: JAMB UTME - Mathematics - 2014 Subject: General Mathematics

Question 1 Report

Evaluate $\int (2 x + 3)^{\frac{1}{2}} δ x$

\frac{1}{12} (2 x + 3)^{6} + k

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

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

\frac{1}{12} (2 x + 3)^{\frac{3}{4}} + k

Answer Details

$\int (2 x + 3)^{\frac{1}{2}} δ x$
let u = 2x + 3, $\frac{δ y}{δ x} = 2$
$δ x = \frac{δ u}{2}$
Now $\int (2 x + 3)^{\frac{1}{2}} δ x = \int u^{\frac{1}{2}} . \frac{δ x}{2}$
$= \frac{1}{2} \int u^{\frac{1}{2}} δ u$
$= \frac{1}{2} u^{\frac{3}{2}} \times \frac{2}{3} + k$
$= \frac{1}{3} u^{\frac{3}{2}} + k$
$= \frac{1}{3} (2 x + 3)^{\frac{3}{2}} + k$

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Integration

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