IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 30

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Area Under Curves, with the answer and a step-by-step solution.

Area Under CurvesCalculusMultiple choiceMedium
What is the total area enclosed between the curves y = |x| and y ={x}^{2}- 2?
  1. A
    \frac{20}{3} square units
  2. B
    \frac{16}{3} square units
  3. C
    8 square units
  4. D
    \frac{10}{3} square units
Pick an option, then check.
Answer & solution

Answer: Option A

Both curves are symmetric about the y-axis, so find the area for x ≥ 0 and double it.

For x ≥ 0, |x| = x, so the curves meet where x = x² − 2, that is x² − x − 2 = 0.

Factorising: (x − 2)(x + 1) = 0, so x = 2 is the relevant root.

Between x = 0 and x = 2 the line y = x lies above the parabola — at x = 0 the values are 0 and −2.

Area for x ≥ 0 = ∫₀² (x − x² + 2) dx = [x²/2 − x³/3 + 2x]₀².

That equals 2 − 8/3 + 4 = 6 − 8/3 = 10/3.

Doubling for the left half gives a total area of 20/3 square units.

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