Most Important Selected Qs for JEE AdvancedMathematicsIndefinite Integration

If f(x)= x , g(x)=e^x-1 , and f g(x) d x=A f g(x)+B ⁻¹(f g(x))+C , then A+B is equal to

Options

A1
B2
C3
Dnone of these

Correct answer

D. none of these

Step-by-step solution

f o g(x)= e^x-1 aligned & I= e ^ x -1 dx = 2 t ^2 t ^2+1 dt ( where e ^ x -1 = t ) & =2 t -2 ⁻¹ t + C =2 e ^ x -1 -2 ⁻¹ ( e ^ x -1 )+C=2 f o g( x )-2 ⁻¹( fog ( x ))+C & A + B =2+(-2)=0 aligned

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