TS EAMCET · Maths · Definite Integration
If \(f(x)=\left|\begin{array}{ccc}1+\sin x+\sin 2 x+\sin 3 x & \frac{3+\sin 2 x}{2} & \frac{-2+\sin 3 x}{3} \3+4 \sin x & \frac{3}{2} & \frac{4}{3} \sin x \1+\sin x & \frac{1}{2} \sin x & \frac{1}{3}\end{array}\right|\) then \(\int_0^{\pi / 2}\left(f(x)+f^{\prime}(x)\right) d x=\)
- A \(\frac{-1}{6}\)
- B \(\frac{-1}{9}\)
- C \(\frac{-2}{9}\)
- D \(\frac{1}{27}\)
Answer & Solution
Correct Answer
(B) \(\frac{-1}{9}\)
Step-by-step Solution
Detailed explanation
Given that, \(f(x)=\left|\begin{array}{ccc}1+\sin x+\sin 2 x+\sin 3 x & \frac{3+\sin 2 x}{2} & \frac{-2+\sin 3 x}{3} \\ 3+4 \sin x & \frac{3}{2} & \frac{4}{3} \sin x \\ 1+\sin x & \frac{1}{2} \sin x & \frac{1}{3}\end{array}\right|\) \(C_1 \rightarrow C_1-2 C_2-3 C_3\)…
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