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Math 166Z Homework # 4.5 Ungraded 1. Evaluate the following Integrals: Z 4 √ x dx (a) 1 x+1 Z √ 3 x+1 √ (b) dx 3 x−1 Z dx (c) (Hint: try completing the square) (x2 + 2x + 2)2 Z dy (d) 4 y − y2 Z 2 3 x + x2 − 12x + 1 (e) dx x2 + x − 12 0 Z 1 (f) dx (x − 1)3 Z 1 dx (g) x(x + 1)(2x + 3) Z 1 r dr (h) 2 0 r + 4r + 4 2. Choose 5 problems at random from the last page of the document StrategiesForIntegration Stewart.pdf posted on WebCT. Try to do them without looking at your notes or book. 3. A tank has the shape of an inverted circular cone with a height of 20m and a base radius of 8m. It is filled with water to a height of 16m. Find the work required to empty the tank by pumping all of the water to the top of the tank. (The density of water is 1000kg/m3 ) 4. Find the centroid of the region bounded by the curves y = sin x, y = cos x, x = 0, x = π4 . Z 5. Evaluate the integral tan3 t sec4 t dt (a) Once you have done the integral, can you think of another way to do it? (i.e. can you get it to work choosing a different u?) (b) Your answers will look different using the two different methods. Convince yourself they are the same. (What are some different ways you could do this?)