U = COS dv = COS I dI du (n - 1) cos"-2 x dx U = sin x Sandy is off to a bad start, having made an error from which it is nearly impossible to recover. In one sentence, explain Sandy's error. Problem (2): Evaluate the following integrals. Note: some integrals may not require integration by parts. 2a cos(3x) dx / (c) .3 (a) 0. 2x tan-(x2) dx (e) dx (f) z(In 3z)2 dz (Hint: start with (d) / e3 tan(e) dx c* (b) / t² sin(3t) dt the u-sub u = In 3z.) %3D Problem (3): There are plenty of integrals whose evaluations require the applications of more than one technique of integration. Sometimes the steps are straightforward, sometimes not so straightforward. Each of the following integrals can be evaluated by first making a substitution and then applying a second technique of integration.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Parts A, B, and C please
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