Note, in particular, that integration ‘by inspection’ (i.e., writing down the answer and differentiating it to show that it is correct) is not a valid method in answering the question.
You may quote without proof the formula for integration by parts, and the formula for integrals of the form ∫ f ′ (x)/f(x) dx, but, if used, your working should include an explicit statement of the formula the first time it is used in each question. If a particular formula is required more than once in a given question, you should also explicitly mention the formula each time it is used subsequently (e.g., justify a subsequent step in your argument by saying “...using the formula for integration by parts”)
You may assume, without ever mentioning, the linearity property of the integral
Note that you may not assume without proof any other integrals.
Transcribed Image Text:I.
In x
dx
3
II.
x² cos(2x) dx
III.
cos x dx
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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