Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

If I_r= _a^ +a | 1 r x+ 1 r+1 x | d x where a R and r N , then _ n _ r=1 ^n (I_r^2- 8 (r+1)^2 ) equals:

Correct answer

Step-by-step solution

aligned I_r & =2 1 r^2 + 1 (r+1)^2 I_r^2 & = 4 r^2 + 4 (r+1)^2 I_r^2- 8 (r+1)^2 & = 4 r^2 - 4 (r+1)^2 _ r=1 ^n (I_r^2- 8 (r+1)^2 ) & =4 ( 1 1^2 - 1 (r+1)^2 ) _ n _ r=1 ^n (I_r^2- 8 (r+1)^2 ) & =4 aligned

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