Evaluate ∫(e^(2/w))/(w²) dw

JAMB Mathematics 2024 302 views
Source: JAMB · 2024

Evaluate ∫(e^(2/w))/(w²) dw

  1. -1/(2w) × e^(2/w) + c
  2. -1/2 × (e^(2/w))/(2w) + c
  3. -1/2 × e^(2/w) + c ✓
  4. -1/2 × (e^(2/w))/(w²) + c
Explanation

Use substitution. Let u = 2/w. Then du/dw = -2/w², so du = -2/w² dw and dw/w² = -du/2.

The integral becomes -1/2 ∫e^u du = -1/2 e^u + c.

Put u = 2/w back: -1/2 × e^(2/w) + c. Check by differentiating: -1/2 × e^(2/w) × (-2/w²) = e^(2/w)/w².

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