Unformatted text preview: Do not evaluate the integral. (b) What method did you use to part (a)? 4. (12 points) A bucket full of water is hanging down a well at the end of a 30 ft rope. The bucket and water together weigh 20 lbs. The rope has a density of 0.5 lb/ft. Set up an integral for calculating how much work is done lifting the bucket to the top of the well. Do not evaluate the integral. 5. (20 points) Evaluate each of the following deﬁnite integrals: (a) Z π/ 2 sin 2 x cos xdx (b) Z π/ 4 tan 2 θ sec 4 θ dθ 6. (24 points) Find the following indeﬁnite integrals: (a) Z x 2 ln xdx (b) Z 1 √ x 2 + 4 dx (c) Z x 2 √ 16-x 2 dx 7. (6 points) Find the following indeﬁnite integral Z √ x 2 + 4 x + 5 dx...
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- Spring '10
- following indeﬁnite integrals, following definite integrals