Evaluate: ₀^ 1 5+4 x d x

Step-by-step solution

We have, ₀^ 1 5+4 x d x= ₀^ 1 5+4 ( 1- ² x 2 1+ ² x 2 ) d x= ₀^ 1+ ² x 2 5 (1+ ² x 2 )+4 (1- ² x 2 ) d x= ₀^ 1+ ² x 2 9+ ² x 2 dx = ₀^ ² x 2 9+ ² x 2 dx Let x 2 =t 1 2 ² x 2 d x=d t Also, x=0 t=0 and x= t= I = ₀^ dt 9+t² I =2 ₀^ dt 9+t² I = 2 3 [ ⁻¹ t 3 ]₀^ = 2 3 [ ⁻¹ - ⁻¹ 0 ]= 2 3 ( 2 -0 )= 3