Homework 16: Integration problems

Exercise 1 . Find the anti-derivative of each of the following:

(a) ;
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(b) ;
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(c)

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(d) ;
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(e) ;
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(f) ;

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(g) ;
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(h) ;
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(i) ;
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(j) .

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Exercise 2 . Suppose that the term were absent in the numerator of Example 4 b. Find the anti-derivative by substituting and then using the formula for the derivative of .
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Exercise 3 . Find the formula for for a falling body if you know and ) at some time (not necessarily at time 0 ).
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Exercise 4. Find the distance function if and both velocity and distance are zero at time .
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Exercise 5. Find the distance function if the acceleration function is given by the following formula, and if the initial velocity and the initial distance at time are known:
(a) (where is a constant);
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(b) ;

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(c) ;
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(d) .
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