If ₀^ / 2 dx 3 x +5 = k ⁻¹ ⁻¹ 2 , then what is the value of K ?

Step-by-step solution

aligned & I= ₀^ / 2 d x 3 x+5 & I= ₀^ / 2 d x 3 [ 1- ^2 x 2 1+ ^2 x 2 ]+5 aligned aligned & I= ₀^ / 2 (1+ ^2 x 2 ) d x 3-3 ^2 x 2 +5+5 ^2 x 2 & I= ₀^ / 2 ^2 x 2 d x 2 ^2 x 2 +8 & I= 1 2 ₀^ / 2 ^2 x 2 d x ^2 x 2 +2^2 aligned Put x 2 =y aligned & 1 2 ^2 x 2 d x=d y & I= ₀^1 d y y^2+2^2 & I= 1 2 ⁻¹ ( y 2 ) & I= 1 2 ⁻¹ ( 1 2 )-0 aligned Also I= 1 2 ⁻¹ 1 2 =k ⁻¹(2) aligned & ( ⁻¹(x)= ⁻¹ ( 1 x ) ) & 1 2 ⁻¹ ( 1 2 )=k ⁻¹ ( 1 2 ) & k= 1 2 aligned