CBSE Class 12 Mathematics sample paper 2024-25: question 29(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. Using ${\int }_0^{a}f(x)dx={\int }_0^{a}f(a-x)dx$: $I={\int }_0^1(1-x)\{1-(1-x){\}}^{n}dx={\int }_0^1{x}^n(1-x)dx$.

   1 mark

2. $I={\int }_0^1{x}^{n}dx-{\int }_0^1{x}^{n+1}dx$.

   ½ mark

3. $=\frac{1}{n+1}[x^{n+1}{]}_0^1-\frac{1}{n+2}[x^{n+2}{]}_0^1$.

   ½ mark

4. $=\frac{1}{n+1}-\frac{1}{n+2}=\frac{1}{(n+1)(n+2)}$.

   1 mark

Answer: $\frac{1}{(n+1)(n+2)}$

Revise the chapter

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