₀^ ⁴ x ⁴ x+ ⁴ x d x is equal to

Step-by-step solution

Let, I= ₀^ ⁴ x ⁴ x+ ⁴ x d xI=2 ₀^ / 2 ⁴ x ⁴ x+ ⁴ x d x...(i) [ ₀^ 2 a f(x) d x=2 ₀^ a f(x) d x . , if .f(2 a-x)=f(x) ] aligned & I=2 ₀^ / 2 ⁴ ( 2 -x ) ⁴ ( 2 -x )+ ⁴ ( 2 -x ) d x & I=2 ₀^ / 2 ⁴ x ⁴ x+ ⁴ x d x...(ii) aligned On adding Eqs. (i) and (ii), we get aligned 2 l &=2 ₀^ / 2 ⁴ x+ ⁴ x ⁴ x+ ⁴ x d x &=2 ₀^ / 2 d x=2[x]₀^ r =2 ( 2 -0 ) 2 l &= l= 2 aligned