# hw2 - R r ( t ) dt and then use the fact that r (0) = 0 to...

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Math 116 Homework #2 1. Find the derivative of f ( x ) = ( x - 1)( x 2 - 9)( x 3 + 2) 2. Find the indeﬁnite integral R xe x 2 dx 3. In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that is circular in shape. If the radius r of the circle is increasing at the rate of r 0 ( t ) = 30 2 t + 4 feet per minute at t minutes after the rupture occurs, ﬁnd an expression for the radius at time t , given that r (0) = 0. How large is the polluted area 16 minutes ( t = 16) after the rupture occurred? Hint: Integrate
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Unformatted text preview: R r ( t ) dt and then use the fact that r (0) = 0 to solve for C , the constant of integration. 4. Linear functions often are good choices for u when integrating by substitution. Suppose that R f ( u ) du = F ( u ) + C . Show that Z f ( ax + b ) dx = 1 a F ( ax + b ) + C 5. Find the indenite integral Z e 3 x +5 + 1 2 x-1 dx Hint: Use the fact you just showed in problem 4 to avoid having to explicitly show a substitution step if you understand it....
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## This note was uploaded on 04/06/2010 for the course MATH 116 taught by Professor Scholle,minho during the Spring '08 term at Kansas.

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