KCET2021MathematicsDefinite Integration
If I_ n = ₀^ 4 ^ n x d x , where n is positive integer, then I₁₀+I₈ is equal to
Options
- A9
- B1 7
- C1 8
- D1 9
Correct answer
D. 1 9
Step-by-step solution
I_ n = ₀^ 4 ^ n x d x...(i)I_ n+2 = ₀^ 4 ^ n+2 x d x...(ii) Adding Eqs. (i) and (ii), aligned I_ n +I_ n+2 &= ₀^ 4 ^ n x d x+ ₀^ 4 ^ n+2 x d x &= ₀^ 4 ^ n x ² x d x &= [ ^ n+1 x n+1 ]₀^ 4 = 1 n+1 aligned Thus, I_ n +I_ n+2 = 1 (n+1) Substitute 8 for x , I₈+I₁₀= 1 9