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
- A -15
- B \(-\frac{15}{2}\)
- C -30
- D -5
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 \(C_2 \rightarrow C_2-C_1\) ]…
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