Question on: JAMB Mathematics - 2014
Evaluate (\int (2x + 3)^{\frac{1}{2}} \delta x)
A
\(\frac{1}{12} (2x + 3)^6 + k\)
B
\(\frac{1}{3} (2x + 3)^{\frac{1}{2}} + k\)
C
\(\frac{1}{3} (2x + 3)^{\frac{3}{2}} + k\)
D
\(\frac{1}{12} (2x + 3)^{\frac{3}{4}} + k\)
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Correct Option: C
(\int (2x + 3)^{\frac{1}{2}} \delta x)
let u = 2x + 3, (\frac{\delta y}{\delta x} = 2)
(\delta x = \frac{\delta u}{2})
Now (\int (2x + 3)^{\frac{1}{2}} \delta x = \int u^{\frac{1}{2}}.{\frac{\delta x}{2}})
( = \frac{1}{2} \int u^{\frac{1}{2}} \delta u)
( = \frac{1}{2} u^{\frac{3}{2}} \times \frac{2}{3} + k)
( = \frac{1}{3} u^{\frac{3}{2}} + k)
( = \frac{1}{3} (2x + 3)^{\frac{3}{2}} + k)
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