Question

If $A={\int }_0^1{x}^{50}(2-x{)}^{50}dx,B={\int }_0^1{x}^{50}(1-x{)}^{50}dx$, which of the following is true?

• A. $A=2^{50}B$
• B. $A=2^{-50}B$
• C. $A=2^{100}B$
• D. $A=2^{-100}B$

Answer 1

Answer: (A)

$A=2^{50}B$

Solution : - given,

$\Rightarrow A={\int }_0^1{x}^{50}(2-2x{)}^{50}dx$ $B={\int }_0^1{x}^{50}(1-x{)}^{50}dx$

$\Rightarrow A={\int }_0^1{x}^{50}\times 2^{50}(1-x{)}^{30}dx$

$\Rightarrow A=2^{50}{\int }_0^1{x}^{50}(1-x{)}^{50}dx$

$\Rightarrow A=2^{50}B$ proved