Questions from General Calculus


Q: Generalize the result of Exercise 73 as follows: Let n be

Generalize the result of Exercise 73 as follows: Let n be a positive integer. Show that 0∫1 (n√x – xn) dx = (n-1)/(n+1).

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Q: Calculate the following integrals. ∫32 dx

Calculate the following integrals. ∫32 dx

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Q: Calculate the following integrals. ∫ (x2 - 3x +

Calculate the following integrals. ∫ (x2 - 3x + 2) dx

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Q: Calculate the following integrals. ∫ 2x + 1 dx

Calculate the following integrals. ∫ 2x + 1 dx

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Q: Calculate the following integrals. ∫ 2/(x + 4

Calculate the following integrals. ∫ 2/(x + 4) dx

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Q: Calculate the following integrals. ∫ (x3 + 3x2 -

Calculate the following integrals. ∫ (x3 + 3x2 - 1)dx

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Q: Find the value of k that makes the antidifferentiation formula true.

Find the value of k that makes the antidifferentiation formula true. ∫3/(2 + x) dx = k ln |2 + x| + C

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Q: Find the value of k that makes the antidifferentiation formula true.

Find the value of k that makes the antidifferentiation formula true. ∫5/(2 - 3x) dx = k ln |2 - 3x| + C

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Q: Find all functions f (t) that satisfy the given condition

Find all functions f (t) that satisfy the given condition. f ‘(t) = t3/2

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Q: Find all functions f (t) that satisfy the given condition

Find all functions f (t) that satisfy the given condition. f ‘(t) = 4/(6 + t)

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