AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{d x}{(x-1)^{3 / 2}(x-3)^{1 / 2}}=\sqrt{f(x)}+c\) then \(f(-1)-f(0)=\)
- A -3
- B -4
- C -2
- D -1
Answer & Solution
Correct Answer
(D) -1
Step-by-step Solution
Detailed explanation
Let \(x-1 = \frac{1}{t} \implies dx = -\frac{1}{t^2} dt\). \(x-3 = x-1-2 = \frac{1}{t}-2 = \frac{1-2t}{t}\). \(\int \frac{dx}{(x-1)^{3/2}(x-3)^{1/2}} = \int \frac{-\frac{1}{t^2}}{(\frac{1}{t})^{3/2}(\frac{1-2t}{t})^{1/2}} dt\).…
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