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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)
Correct Answer: Option C
Explanation

(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)

There is an explanation video available below.

Explanation Video