MATH 1210 (Calculus I) - 5.1 to 5.5 Review + Bonus Questions

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This is a small review of sections 5.1 to 5.5.  You can view the Course Outline to check what these sections are about.

Here's a "human readable" version of this review:
Math 1210 - Calculus I - Section 5 and Bonus

Problems - Web version.

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1. (5.1) Given y=(2/3)x, y=0, x=3.  Find the are of the enclosed shape with respect to x.

2. (5.1) Given y=(2/3)x, y=0, x=3. Find the are of the enclosed shape with respect to y.

3. (5.2) Given y=(2/3)x, y=0, x=3. Find the volume of the shape using disk/washer method by rotating around the x-axis.

4. (5.3) Given y=(2/3)x, y=0, x=3. Find the volume of the shape using cylindrical method by rotating around the x-axis.

5. (5.2) Given y=(1/4)x^2, x=2, y=0. Find the volume of the shape using disk/washer method by rotating around the y-axis.

6. (5.3) Given y=(1/4)x^2, x=2, y=0. Find the volume of the shape using the cylinder method by rotating around the y-axis.

7. (5.4) A variable force of 5x^-2 pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from x=1 ft to x=10 ft.

8. (5.4) Spring example. A force of 10 lbs is required to hold a spring stretched 4 inches beyond its natural length. How much work is done in stretching it from its natural length to 6 inches beyond its natural length?

9. (5.4) You are pulling a 0.5 lb rope, that is 50 ft long.  How much work does it take to pull half the rope.

10. (5.4) You are pulling a 2 lb rope, that is 500 ft long, with the addition of a 800 lb box.  How much work does it take to pull the entire rope.

11. (5.4) You are pumping water from the top side of a tank.  The tank's dimensions are 2m x 1m x 1m (wlh).  How much work does it take to pump half the water.

12. (5.5) Given f(x)=4x-x^2. What is the average value of the function on the interval [0,4].

Earlier Chapters

13. (2.8) A plane is flying 6 miles above earth, and the distance between the plane and the radar station is changing at a rate of 240 mph.  When the plane is 10 miles away from the radar station, how fast will the plane be travelling?

14. (2.8) A cone shaped tank is being filled with water at a rate of 2 m^3/min.  The tank's dimensions are 2m radius, and 4m in height.  Find the rate at which the water level is rising when h = 3m.

15. (3.7) Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.

16. Solve the integrals: (a) integral(1/(1+x^2), x);  (b) integral(1/sqrt(1-x^2), x);  (c) integral(-1/sqrt(1-x^2), x);  (d) integral(1/x, x);  (e) integral(e^(ax), x);  (f) integral(e^(-5x), x);  (g) integral((x-3)/root(x, 3), x).


Solutions

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Stewart's Calculus 7E, MS Mathematics, Wolfram Alpha.
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