Explanation Given: The integral ∫ d x 4 − x , x ≠ 4 . Formula used: ∫ 1 x d x = ln x + C Calculation: Evaluate the integral ∫ d x 4 − x . Let 4 − x = u . Then, − d x = d u . So, d x = − d u . Substitute 4 − x = u and d x = − d u in the integral and evaluate it. ∫ d x 4 − x = ∫ − 1 u d u = − 1 ⋅ ∫ 1 u d u = − ln u + C Substitute u = 4 − x

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Chapter 4.5, Problem 24E

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To evaluate: The integral ∫dx4−x,x≠4 .

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Chapter 4.5, Problem 23E

Chapter 4.5, Problem 25E

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The integral ∫ d x 4 − x , x ≠ 4 .

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To evaluate: The integral ∫dx4−x,x≠4 .

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