Questions from General Calculus


Q: By completing the square in the quadratic 3 – 2x – x2

By completing the square in the quadratic 3 – 2x – x2 and making a trigonometric substitution, evaluate.

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Q: (a). Use the reduction formula in Example 6 to show

(a). Use the reduction formula in Example 6 to show that fπ/20 sinnx dx = n – 1/n, fπ/20 sinn-2x dx where n > 2 is an integer. (b). Use part (a) to evaluate...

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Q: Prove that, for even powers of sine, /

Prove that, for even powers of sine,

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Q: Use Exercise 39 to find f (ln x)3 dx

Use Exercise 39 to find f (ln x)3 dx. Exercise 39: f (ln x) n dx = x (ln x) n – n f (ln x) n-1 dx

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Q: Find the volume common to two spheres, each with radius r

Find the volume common to two spheres, each with radius r, if the center of each sphere lies on the surface of the other sphere.

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Q: Use Exercise 40 to find f x4 ex dx.

Use Exercise 40 to find f x4 ex dx. Exercise 40: f xn ex dx = xn ex – n f xn-1 ex dx

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Q: Use the Table of Integrals on Reference Pages 6–10 to

Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral.

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Q: Use the Table of Integrals on Reference Pages 6–10 to

Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral.

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Q: Use the Table of Integrals on Reference Pages 6–10 to

Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral.

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Q: Use the Table of Integrals on Reference Pages 6–10 to

Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral.

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