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.

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.