CBSE Class 12 Mathematics 2026: question 27(b)

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Complete the square: $x^2+2x+3=(x+1{)}^2+(\sqrt{2}{)}^2$, so $I={\int }_0^2\frac{dx}{\sqrt{(x+1{)}^2+(\sqrt{2}{)}^2}}$

   1 mark

2. Using $\int \frac{dx}{\sqrt{t^2+a^2}}=\log |t+\sqrt{t^2+a^2}|$:

   $I={\left[\log \left(x+1+\sqrt{x^2+2x+3}\right)\right]}_0^2$

   1 mark

3. $I=\log (3+\sqrt{11})-\log (1+\sqrt{3})=\log \left(\frac{3+\sqrt{11}}{1+\sqrt{3}}\right)$

   1 mark

Answer: $\log \left(\frac{3+\sqrt{11}}{1+\sqrt{3}}\right)$

Revise the chapter

• Chapter: Integrals (notes, formulas, where marks are lost and every past question)