Integral Calculus & Area · NDA previous year questions

2025 7 questions

1. Q742025 · 14 Sept 2025

   For the following three (03) items: Consider the function f(x) = x|x| What is the area bounded by the curve f(x) the x-axis and the lines x = - 2 and x = 1

   1. A.1/3
   2. B.2/3
   3. C.5/2
   4. D.3
   Show answer

   Answer: D

2. Q982025 · 14 Sept 2025

   What is the area of the region bounded by |x| <= 2k and |y| <= k where k is a positive real number?

   1. A.$2k^2$
   2. B.$4k^2$
   3. C.$5k^2$
   4. D.$8k^2$
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   Answer: D

3. Q782025 · 13 Apr 2025
   Passage

   Consider the following for the two (02) items that follow: The slope of the tangent to the curve y = f(x) at (x, f(x) ) is 4 for every real number x and the curve passes through the origin.

   . What is the area bounded by the curve, the x-axis and the line x = 4?

   1. A.8 square units
   2. B.16 square units
   3. C.32 square units
   4. D.64 square units
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   Answer: C

4. Q822025 · 13 Apr 2025

   Consider the following for the two (02) items that follow: Let the function $y=(1-\cos x{)}^{-1}$ where $x\ne 2n\pi$ and n is an integer What is $\int ydx$ equal to? where c is the constant of integration.

   1. A.$-\tan (x/2)+c$
   2. B.$-\cot (x/2)+c$
   3. C.$\tan (x/2)+c$
   4. D.$\cot (x/2)+c$
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   Answer: B

5. Q862025 · 13 Apr 2025
   Passage

   Consider the following for the two (02) items that follow: Let the curve f(x) = |x - 3|

   What is the area bounded by the curve f(x) and y = 3?

   1. A.3 square units
   2. B.4.5 square units
   3. C.7.5 square units
   4. D.9 square units
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   Answer: D

6. Q872025 · 13 Apr 2025
   Passage

   Consider the following for the two (02) items that follow: Let f = {(1, 1), (2, 4), (3, 7), (4, 10)}

   If f(x) = px + q then what is the value of (p + q) ?

   1. A.-1
   2. B.0
   3. C.1
   4. D.5
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   Answer: C

7. Q902025 · 13 Apr 2025

   Consider the following for the two (02) items that follow : Let the function $f(x)=x^2-1$ What is the area bounded by the function $f(x)$ and the x-axis?

   1. A.1/3 square unit
   2. B.2/3 square unit
   3. C.4/3 square units
   4. D.2 square units
   Show answer

   Answer: C