Evaluate ∫(1 + w)(2w + w²)⁵ dw

JAMB Mathematics 2024 303 views
Source: JAMB · 2024

Evaluate ∫(1 + w)(2w + w²)⁵ dw

  1. 1/12 (1 + w)⁶
  2. 1/12 (2w + w²)⁶ ✓
  3. 1/12 (1 + w)(2w + w²)⁶
  4. 1/12 (w + w²)⁵
Explanation

Use substitution. Let u = 2w + w². Then du/dw = 2 + 2w = 2(1 + w), so (1 + w) dw = du/2.

The integral becomes ∫ u⁵ × (du/2) = (1/2) × u⁶/6 = u⁶/12.

Put u back: 1/12 (2w + w²)⁶ (+ C).

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