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Unformatted text preview: Review Sheet for First Exam Mathematics 2300 September 20, 2006 The exam will cover Sections 6.9, 1.8, 7.4, 7.5, 7.6, and 7.7. In addition there will be some problems on substitutions (6.3 and 6.8). No calculators of any kind will be allowed. Formulas to remember: Standard indefinite integrals Z x n dx = x n +1 n + 1 + C, ( n 6 =- 1) Z 1 x dx = ln | x | + C Z e x dx = e x + C Z cos x dx = sin x + C Z sin x dx =- cos x + C Z sec 2 x dx = tan x + C Z sec x tan x dx = sec x + C Z 1 1 + x 2 dx = arctan x + C Z 1 1- x 2 dx = arcsin x + C The Fundamental Theorem of Calculus: If f is continuous at x , then d dx Z x a f ( t ) dt = f ( x ) . If f is continuous in [ a, b ], then Z b a f ( x ) dx = f ( b )- f ( a ) . Also understand how to use the chain rule here to compute, e.g., d dx Z x 2 x f ( t ) dt. 1 Length of a parametric curve: if x ( t ) and y ( t ) are continuous, then L = Z b a s dx dt 2 + dy dt 2 dt. Understand how to derive the formula for length of y = f ( x ) by using the standard parametrization x = t , y = f ( t ). (Similarly if x = f ( y ), use x = f ( t ) , y = t .) Dont memorize three different formulas for arc length!memorize three different formulas for arc length!...
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