(a) Evaluate: (int limits_1^2 (2x^3 – 4x + 3) dx)
(b) Given that P(^{-1}) = (begin{pmatrix} -1 & 1 \ 4 & -3 end{pmatrix}), find the matrix P.
Explanation
(a). They integrated the given function correctly to obtain ((frac{x^4}{2} – 2x^2 + 6x)). Substituting the limits 2 and 1 for x and simplifying yielded 12 – (frac{9}{2}) = 7(frac{1}{2})
(b). Find the determinant of which was P((^{-1}))(^{-1}) = |P=(^{-1})| (-3 x -1) – (4 x 1) = -1.
Using the concept of P((^{-1}))(^{-1}) = P, then, P = -1 (begin{pmatrix} -3 & -1 \ 4 & -3 end{pmatrix}) = (begin{pmatrix} 3 & 1 \ 4 & 1 end{pmatrix})