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AP EAMCET · Maths · Definite Integration

\(\int_{\frac{1}{25}}^3 \frac{e^{\frac{3}{x}}}{x^2} d x=\)

  1. A \(-\frac{1}{3}\left(e^{75}-e\right)\)
  2. B \(\frac{1}{3}\left(e^{50}-e^{25}\right)\)
  3. C \(-\frac{1}{3}\left(\mathrm{e}^{50}-\mathrm{e}\right)\)
  4. D \(\frac{1}{3}\left(e^{75}-e\right)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{3}\left(e^{75}-e\right)\)

Step-by-step Solution

Detailed explanation

Let \(I=\int_{\frac{1}{25}}^3 \frac{e^{\frac{3}{x}}}{x^2} d x\) Let \(\frac{3}{x}=t\) \(\Rightarrow-\frac{3}{x^2} d x=d t \Rightarrow \frac{1}{x^2} d x=-\frac{1}{3} d t\) When \(x=3 \Rightarrow t=1\)…