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# Colby College Some Handy Integrals Gaussian Functions f dx f x e dx a f dx a f dx a f dx a f dx f n dx n n f n dx n n Exponential Functions f ax n n ntegrals from f to f Even and Odd Funct PDF document - DocSlides

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### Presentations text content in Colby College Some Handy Integrals Gaussian Functions f dx f x e dx a f dx a f dx a f dx a f dx f n dx n n f n dx n n Exponential Functions f ax n n ntegrals from f to f Even and Odd Funct

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Colby College Some Handy Integrals Gaussian Functions f dx = f x e dx = 2a f dx = 4a f dx = 2a f dx = 8a f dx = f 2n dx = 1·3·5··· 2n n+1 f 2n+1 dx = n! n+1 Exponential Functions f ax = n! n+1 ntegrals from f to f : Even and Odd Functions The i ntegra l of any even function take n between the limits f to f is twice the integral from 0 to f . The integral of any odd function between f and f is equal to zero, see Figure 1. (a) . (x) (b) . (x) (x) ] x e even odd even Figure 1. Even and odd integrals. o determine if a function is even, check to see if f(x) = f( x). For an odd function, f(x) = f( x). Some funct ions are neither odd nor even. For example, f(x) x is odd, f(x) is even, and f(x) is neither odd nor even. he following multipli cation rules hold: even*even even odd*odd =e ven odd*even odd onsider the integral of (x) , Figure 1a The function is even so that f f = 2 f Next consider (x) , which is odd , giving (x) (x) ] = x e s overall odd (Figure 1 ). The integral is zero for the product function. even integrals add odd integrals cancel

The integral of any odd function between f and f is equal to zero see Figure 1 a x b x x x e even odd even Figure 1 Even and odd integrals o determine if a function is even check to see if fx f x For an odd function fx f x Some funct ions are n ID: 23300

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Colby College Some Handy Integrals Gaussian Functions f dx = f x e dx = 2a f dx = 4a f dx = 2a f dx = 8a f dx = f 2n dx = 1·3·5··· 2n n+1 f 2n+1 dx = n! n+1 Exponential Functions f ax = n! n+1 ntegrals from f to f : Even and Odd Functions The i ntegra l of any even function take n between the limits f to f is twice the integral from 0 to f . The integral of any odd function between f and f is equal to zero, see Figure 1. (a) . (x) (b) . (x) (x) ] x e even odd even Figure 1. Even and odd integrals. o determine if a function is even, check to see if f(x) = f( x). For an odd function, f(x) = f( x). Some funct ions are neither odd nor even. For example, f(x) x is odd, f(x) is even, and f(x) is neither odd nor even. he following multipli cation rules hold: even*even even odd*odd =e ven odd*even odd onsider the integral of (x) , Figure 1a The function is even so that f f = 2 f Next consider (x) , which is odd , giving (x) (x) ] = x e s overall odd (Figure 1 ). The integral is zero for the product function. even integrals add odd integrals cancel

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