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pls help. For first one, I don't need answer but is integral from -2 to 1 (g(x)-f(x))(x+3)dx set-up right?

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Screen Shot 2019-09-22 at 4.00.50 PM.png

b) (5 pts) A rocket with a mass of 3 tons is filled with 40 tons of liquid fuel. In the initial part of the flight fuel burns at a
rate of 1 ton per 100 meters of vertical height. How much work (in international units) is done by rocket in the first
kilometer of vertical flight? [Hint: use g = 10 m/s, 1 ton = 1,000Kg, 1Km = 1,000m].

Screen Shot 2019-09-22 at 8.43.30 PM.png

5. (10 pts) Using the method of volumes by SHELLS:
(a) write an integral for the solid generated by rotating about the @ = -3 line (note that the line is off-axis!) the
shaded region on the figure [delimited between y = f (x) and y = g(@)].
(b) Sketch the solid and (c) a typical shell for this object.
V3 =
6. (10 pts) Show, using the method of volume by slices, that the volume of a pyramid of height H with a RECTANGULAR
base of size A by B is given by V = ; A x B X H. Draw a diagram including a typical slice for this object.
Clearly indicate the function(s) that you are plotting and the interval of integration.

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