The value of ₃⁴ (4-x)(x-3) d x is

Step-by-step solution

Let I= ₃⁴ (4-x)(x-3) d x= ₃⁴ -x²+7 x-12 d x= ₃⁴ - (x²-7 x+ 49 4 - 49 4 )-12 d x= ₃⁴ - (x- 7 2 )²+ 49 4 -12 d x= ₃⁴ 1 4 - (x- 7 2 )² d x Let t=x- 7 2 d t=d x Upper limit = 1 2 and lower limit =- 1 2 array l = _ -1 / 2 ^ 1 / 2 ( 1 2 )²-t² d t =2 ₀^ 1 / 2 ( 1 2 )²-t² d t =2 [ t 2 1 4 -t² + 1 8 ⁻¹ 2 t ]₀^ 1 / 2 =2 [0+ 1 8 2 ] = 8 array