For 0 x 2 , the value of ₀^ ^2 x ⁻¹( t ) d t+ ₀^ ^2 x ⁻¹( t ) d t equals :

Step-by-step solution

Consider ₀^ ^2 x ⁻¹( t ) d t+ ₀^ ^2 x ⁻¹( t ) d t Let I =f(x) after integrating and putting the limits. aligned &f^ (x)= ⁻¹ ^2 x (2 x x)-0 & + ⁻¹ ^2 x (-2 x x)-0 & f^ (x)=0 f(x)= C (constant) aligned Now, we find f(x) at x= 4 aligned I &= ₀^ 1 / 2 ⁻¹ t d t+ ₀^ 1 / 2 ⁻¹ t d t &= ₀^ 1 / 2 ( ⁻¹ t + ⁻¹ t ) d t &= ₀^ 1 / 2 2 d t= 4 = C f(x)= 4 Required integration = 4 aligned