Integral Calculus & Area · JEE Main previous year questions

2017 3 questions

1. Q122017 · 9 Apr 2017 · Shift 1

   If $f\left(\frac{3x-4}{3x+4}\right)=x+2$, $x\ne -\frac{4}{3}$, and $\int f(x)\mathrm{d}x=\mathrm{A}\log |1-x|+\mathrm{B}x+\mathrm{C}$, then the ordered pair (A, B) is equal to : (where C is a constant of integration)

   1. A.$(\frac{8}{3},\frac{2}{3})$
   2. B.$(-\frac{8}{3},\frac{2}{3})$
   3. C.$(-\frac{8}{3},-\frac{2}{3})$
   4. D.$(\frac{8}{3},-\frac{2}{3})$
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   Answer: B

2. Q122017 · 8 Apr 2017 · Shift 1

   The integral $\int \sqrt{1+2\cot x(\mathrm{cosec}x+\cot x)}dx$ $(0<x<\frac{\pi }{2})$ is equal to : (where C is a constant of integration)

   1. A.$4\log (\sin \frac{x}{2})+C$
   2. B.$2\log (\sin \frac{x}{2})+C$
   3. C.$2\log (\cos \frac{x}{2})+C$
   4. D.$4\log (\cos \frac{x}{2})+C$
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   Answer: B

3. Q132017 · 8 Apr 2017 · Shift 1

   The integral ${\int }_{\frac{\pi }{12}}^{\frac{\pi }{4}}\frac{8\cos 2x}{(\tan x+\cot x{)}^3}dx$ equals :

   1. A.$\frac{15}{128}$
   2. B.$\frac{15}{64}$
   3. C.$\frac{13}{32}$
   4. D.$\frac{13}{256}$
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   Answer: A