\(\int { ({ x }^{ 2 } } +x-1)dx=\int { { x }^{ 2 } } dx+\int { xdx } -\int { dx } \)
\(=\frac { { x }^{ 2+1 } }{ 2+1 } +\frac { { x }^{ 1+1 } }{ 1+1 } -x+c\)
\(=\frac { { x }^{ 3 } }{ 3 } +\frac { { x }^{ 2 } }{ 2 } -x+c\)
 

Given Matrix  A=\(\begin{bmatrix} 3 & 4 \\ 10 & -2 \end{bmatrix}\) then, the Determinant 
\(\left| A \right| =\begin{bmatrix} 3 & 4 \\ 10 & -2 \end{bmatrix}\)=3(-2)-10(4)
= - 6 - 40 = - 46 is the value of the determinant.

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Elasticity of supply is the relative change in supply in response to a relative change in price. If S is supply, the supply function is S = f(p)
The formula for elasticity of supply \(e_{\mathrm{s}}=\frac{\mathrm{P}}{\mathrm{S}} \cdot \frac{\mathrm{ds}}{\mathrm{dp}} ; \frac{\mathrm{ds}}{\mathrm{dp}}=\) slope

\({dq\over dp}=-4-8p\)
R=pq = p(30 - 4p - 4p²)
= 30p - 4p² - 4p³
\(MR={dR\over dq}=30{dp\over dq}-8p{dp\over dq}-12p^2{dp\over dq}\)
\(={1\over -4-8p}(-0-8p-12p^2)\)
\(={1\over 4+8p}(12p^2+8p-30)\)

Ans=\({6p^2+4p-15\over 2+4p}\)