Question

If $\int\limits^{2}_{1} \frac{dx}{\left(x^{2} - 2x + 4\right)^{\frac{3}{2}}} = \frac{k}{k + 5' }$ , then $k$ is equal to :

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

$\int\limits_{1}^{2} \frac{d x}{(x-1)+3)^{3 / 2}}$
$x-1=\sqrt{3} \tan Q$
$=\sqrt{3} \sec ^{2} Q$
$\int\limits_{0}^{\frac{\pi}{6}} \frac{\sqrt{3} \sec d Q}{3 \sqrt{3} \sec .3 Q}$
$=\frac{1}{3} \int\limits_{0}^{\frac{\pi}{6}} \cos esQ =\frac{1}{3}(\tan Q )_{0}^{\pi / 6}$
$=\frac{1}{6}=\frac{k}{k+5}=k+5=k$
$=k=1$