Integral Calculus & Area · NDA previous year questions

2013 8 questions

1. Q882013 · 11 Aug 2013

   What is the area bounded by the lines $x=0,y=0$ and $x+y+2=0$ ?

   1. A.$\frac{1}{2}$ square unit
   2. B.1 square unit
   3. C.2 square units
   4. D.4 square units
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   Answer: C

2. Q922013 · 11 Aug 2013

   What is the area bounded by $y=\tan x,y=0$ and $x=\frac{\pi }{4}$ ?

   1. A.$\ln 2$ square units
   2. B.$\frac{\ln 2}{2}$ square units
   3. C.$2(\ln 2)$ square units
   4. D.None of the above
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   Answer: B

3. Q932013 · 11 Aug 2013

   What is $\int (x\cos x+\sin x)dx$ equal to? where $c$ is an arbitrary constant.

   1. A.$x\sin x+c$
   2. B.$x\cos x+c$
   3. C.$-x\sin x+c$
   4. D.$-x\cos x+c$
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   Answer: A

4. Q942013 · 11 Aug 2013

   What is ${\int }_0^2{e}^{\ln x}dx$ equal to?

   1. A.1
   2. B.2
   3. C.4
   4. D.None of the above
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   Answer: B

5. Q832013 · 14 Apr 2013

   What is $\int e^{\ln x}dx$ equal to ? where c is the constant of integration.

   1. A.$x{e}^{\ln x}+c$
   2. B.$-x{e}^{\ln x}+c$
   3. C.$x+c$
   4. D.$\frac{x^2}{2}+c$
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   Answer: D

6. Q842013 · 14 Apr 2013

   What is ${\int }_{-\pi /6}^{\pi /6}\frac{{\sin }^{5}x{\cos }^{3}x}{x^4}dx$ equal to ?

   1. A.$\frac{\pi }{2}$
   2. B.$\frac{\pi }{4}$
   3. C.$\frac{\pi }{8}$
   4. D.0
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   Answer: Dropped in the final answer key (full marks to everyone)

7. Q852013 · 14 Apr 2013

   What is $\int \frac{dx}{x\ln x}$ equal to ? where c is the constant of integration.

   1. A.$\ln (\ln x)+c$
   2. B.$\ln x+c$
   3. C.$(\ln x{)}^2+c$
   4. D.None of the above
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   Answer: A

8. Q862013 · 14 Apr 2013

   What is the area of the region enclosed by $y=2|x|$ and $y=4$ ?

   1. A.2 square unit
   2. B.4 square unit
   3. C.8 square unit
   4. D.16 square unit
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   Answer: C