Integral Calculus & Area · NDA previous year questions

2019 4 questions

1. Q872019 · 17 Nov 2019

   Directions for the following two (02) items : Read the following information and answer the two items that follow : Consider the integrals $I_1={\int }_0^{\pi }\frac{xdx}{1+\sin x}$ and $I_2={\int }_0^{\pi }\frac{(\pi -x)dx}{1-\sin (\pi +x)}$ What is the value of $I_1$?

   1. A.0
   2. B.$\frac{\pi }{2}$
   3. C.$\pi$
   4. D.$2\pi$
   Show answer

   Answer: C

2. Q882019 · 17 Nov 2019

   Directions for the following two (02) items : Read the following information and answer the two items that follow : Consider the integrals $I_1={\int }_0^{\pi }\frac{xdx}{1+\sin x}$ and $I_2={\int }_0^{\pi }\frac{(\pi -x)dx}{1-\sin (\pi +x)}$ What is the value of $I_1$? What is the value of $I_1+I_2$?

   1. A.$2\pi$
   2. B.$\pi$
   3. C.$\frac{\pi }{2}$
   4. D.0
   Show answer

   Answer: A

3. Q892019 · 17 Nov 2019

   What is the area of the region enclosed between the curve $y^2=2x$ and the straight line $y=x$?

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

4. Q902019 · 17 Nov 2019

   What is the area of the region bounded by $|x|<5$, $y=0$ and $y=8$?

   1. A.40 square units
   2. B.80 square units
   3. C.120 square units
   4. D.160 square units
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   Answer: B