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Unformatted text preview: c = 2000 , or directly c (0) = 2000 Solution We have c ( q ) = Z (2 q + 75) dq = 2 Z q dq + Z 75 dq = q 2 + 75 q + C Since c (0) = 0 2 + 75 · 0 + C and c (0) = 2000 , we have C = 2000 . So c ( q ) = q 2 + 75 q + 2000 . More Integration Formulas Integration by substitution Z f ( u ( x )) · u ( x ) dx = Z f ( u ) du where du = u ( x ) dx Example Z ( x + 5) 11 dx = Z u 11 du where u = x + 5 and du = u ( x ) dx = 1 dx that is du = dx So Z ( x + 5) 11 dx = Z u 11 du = u 12 12 + C = ( x + 5) 12 12 + C Example Find: Z x 3 e x 4 dx Solution Denote u = x 4 ⇒ du = u ( x ) dx that is du = 4 x 3 dx So Z x 3 e x 4 dx = Z e x 4 x 3 dx = 1 4 Z e x 4 4 x 3 dx = 1 4 Z e u du = 1 4 e u + C = 1 4 e x 4 + C...
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This note was uploaded on 12/12/2011 for the course ECON 101 taught by Professor Bi during the Spring '11 term at York University.
 Spring '11
 bi

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