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

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.

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

View answer & explanation

Correct answer is 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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