By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2025 Maths, question 90

Topic: Integral calculus

Passage · Q89 to Q90

Let the function f(x)=x2−1f(x) = x^{2} - 1.

Q90

What is the area bounded by the function and the x-axis?

  1. (a) 1/3 square unit
  2. (b) 2/3 square unit
  3. (c) 4/3 square unitsCorrect answer
  4. (d) 2 square units

Solution.

Answer: (c) 4/3 square units

  1. The intercepts are x=±1x = \pm 1.
  2. Between them, x2−1≤0x^{2} - 1 \leq 0, so geometric area is ∫−11(1−x2) dx\int_{- 1}^{1}\left( 1 - x^{2} \right)\, dx.
  3. Using symmetry, this is 2[x−x3/3]01=4/32\left\lbrack x - x^{3}/3 \right\rbrack_{0}^{1} = 4/3 square units.