MHT CET202620 April 2026Evening ShiftMathematicsDefinite IntegrationActual
If I_n = ₀^ /4 ^n x dx, n N then I_ n+2 + I_n is equal to
Options
- A1 n
- B1 n + 1
- C1 n - 1
- D1 n - 2
Correct answer
B. 1 n + 1
Step-by-step solution
I_ n+2 + I_n = ₀^ /4 ^ n+2 x dx + ₀^ /4 ^n x dx I_ n+2 + I_n = ₀^ /4 ^n x ( ^2 x + 1) dx I_ n+2 + I_n = ₀^ /4 ^n x ^2 x dx Substituting t = x , we get dt = ^2 x dx . When x = 0 , t = 0 and when x = /4 , t = 1 . I_ n+2 + I_n = ₀^1 t^n dt I_ n+2 + I_n = [ t^ n+1 n+1 ]₀^1 I_ n+2 + I_n = 1 n+1 Answer: 1 n + 1