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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Find the value of the definite integral ( 1 ₀^ 2 ^4 x+ x ^3 x+ ^2 x ^2 x+ ^3 x x ^4 x+ ^4 x+2 x ^3 x+2 ^2 x ^2 x+2 ^3 x x d x )⁻¹

Correct answer

4

Step-by-step solution

aligned I & = ₀^ 2 ^4 x+ x ^3 x+ ^2 x ^2 x+ ^3 x x ^4 x+ ^4 x+2 x ^3 x+2 ^2 x ^2 x+2 ^3 x x d x I & = ₀^ 2 ( x ^3 x+ ^3 x x )+ ( ^4 x+ ^2 x ^2 x ) ^4 x+ ^4 x+2 ^2 x ^2 x+ (2 x ^3 x+2 ^3 x x ) d x & = ₀^ 2 x x+ ( ^4 x+ ^2 x ^2 x ) ^4 x+ ^4 x+2 ^2 x ^2 x+2 x x d x aligned Use King and add aligned & 2 I= ₀^ 2 ^4 x+ ^4 x+2 ^2 x ^2 x+2 x x ^4 x+ ^4 x+2 ^2 x ^2 x+2 x x d x= 2 I & = 4 aligned Hence, the given value of definite integral is 4 .

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