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TS EAMCET · Maths · Determinants

If \(A(x)=\left|\begin{array}{ccc}x+1 & 2 x+1 & 3 x+1 \\ 2 x+1 & 3 x+1 & x+1 \\ 3 x+1 & x+1 & 2 x+1\end{array}\right|\), then \(\int_0^1 A(x) d x\) is equal to

  1. A -15
  2. B \(-\frac{15}{2}\)
  3. C -30
  4. D -5
Verified Solution

Answer & Solution

Correct Answer

(B) \(-\frac{15}{2}\)

Step-by-step Solution

Detailed explanation

Since, \[ A(x)=\left|\begin{array}{ccc} x+1 & 2 x+1 & 3 x+1 \\ 2 x+1 & 3 x+1 & x+1 \\ 3 x+1 & x+1 & 2 x+1 \end{array}\right| \] [applying \(C_3 \rightarrow C_3-C_2\) and then \(C_2 \rightarrow C_2-C_1\) ]…