Find `A × B, A × A` and `B × A : A = {1, 2, 3}` and `B = {1, −4}`.

Answer

D

Explanation

`f'(x)=(192x^(3))/2+sin^(4)(pix)AAxepsilonR,f(1/2)=0`
Now, `64x^(3)lef'(x)le96x^(3)AAxepsilon[1/2,1]`
`:.int_(1//2)^(x)64x^(3)dxltint_(1//2)^(x)f'(x)dxleint_(1//2)^(x)96x^(3)dx`
So `16x^(4)-1lef(x)le24x^(4)-3/2AAxepsilon[1/2,1]`
`:.int_(1//2)^(1)(16x^(4)-1)dxleint_(1//2)^(1)f(x)dxleint_(1//2)^(1)f(x)dxleint_(1//2)^(1)(24x^(4)-3/2)dx`
`:. 16/5 . 31/32 - 1/2 le int_(1//2)^(1)f(x)dxle 24/5 . 31/32 -3/4`
`=26/10 le int_(1//2)^(1)f(x)dxle 78/20`