AP EAMCET · Maths · Indefinite Integration
If \(\int\left(3 t^2 \sin \frac{1}{t}-t \cos \frac{1}{t}\right) d t=f(t) \sin \left(\frac{1}{t}\right)+c\), then \(f(2)=\)
- A \(2\)
- B \(-12\)
- C \(8\)
- D \(-16\)
Answer & Solution
Correct Answer
(C) \(8\)
Step-by-step Solution
Detailed explanation
\( \frac{d}{dt} \left( t^3 \sin \left(\frac{1}{t}\right) \right) = 3t^2 \sin \left(\frac{1}{t}\right) + t^3 \cos \left(\frac{1}{t}\right) \left(-\frac{1}{t^2}\right) = 3t^2 \sin \left(\frac{1}{t}\right) - t \cos \left(\frac{1}{t}\right) \)…
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