If ₀¹ f(x) d x=5 , then the value of ...+100 ₀¹ x ⁹ f ( x ¹⁰ ) dx is equal to

Step-by-step solution

Given, ₀¹ f ( x ) dx =5 Let I=100 ₀¹ x⁹ f (x¹⁰ ) d x Put x ¹⁰= t 10 x ⁹ dx = dt I =100 ₀¹ f ( t ) 10 dt =10 5=50 ₀¹ f ( x ) dx +100 ₀¹ x ⁹ f ( x ¹⁰ ) dx =5+50=55