IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 13

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

Definite IntegralsCalculusMultiple choiceMedium
Evaluate: \int_{0}^{1}{\frac{x}{1 +{x}^{2}}dx}.
  1. A
    \frac{1}{4}ln2
  2. B
    \frac{1}{2}ln2
  3. C
    \frac{1}{2}
  4. D
    ln2
Pick an option, then check.
Answer & solution

Answer: Option B

Substitute u = 1 + x², so that du = 2x dx and x dx = du/2.

When x = 0, u = 1; when x = 1, u = 2.

The integral becomes ½ ∫ du/u from u = 1 to u = 2.

That evaluates to ½ [ln u] from 1 to 2 = ½ (ln 2 − ln 1).

Since ln 1 = 0, the answer is ½ ln 2.

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