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# Week 1 Notes Calc II MATH 142 001

UTK

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This 2 page Class Notes was uploaded by Jared Hopland on Thursday January 21, 2016. The Class Notes belongs to MATH 142 001 at UTK taught by Dr. Stephenson in Spring 2016. Since its upload, it has received 110 views. For similar materials see Calculus II in Applied Mathematics at UTK.

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Date Created: 01/21/16

Week 1 Notes Calc II 1/19/16 Anti-Derivative F(x) is the derivative of f(x) on so2e interval F’(x)=f(x) for all x in (a,b). Ex: if f x)=6x then F(x)=3x +k (k being a constant number) If F(x) is the anti-derivative of f(x), then any other antiderivative, G(x), of f(x) G x)=F (x)+k is of the form ∫ f (x)dx is the general antiderivative of f(x). ¿ dx ∫ ¿ Means the indefinite integral of___ Power Rule n+1 x dx= x n ≠−1 ∫ n+1 for any ∫ x dx=ln | |k Linearity Rule f( )+g( )dx= f( )dx+ g ( )x ∫ ∫ ∫ ∫ k∗f (x)dx=k∗ ∫ f (x)dx −2 3 5x +3x dx=5 x dx+33 x dx=5 x +3 x +k Ex: ∫ ∫ ∫ −2 3 Calc I Review Ex: sin(y=x+cos(x) find y' ' ' 1−sin (x) cosy ∗y =1−sin (x=¿y= cos(y) ¿xy∨¿ Ex: state domain in set builder notation. log¿ Dom={(x,y)∨x≠0∧y≠0} Trig Functions ∫ si( ) dx=−cos( )+k ∫ cos( )dx=sin( )+k 2 ∫ sec( )dx=tan( )+k ∫ csc( )dx=−cot ( )k ∫ sec( )ta( ) dx=se( ) +k ∫ csc( )co( ) dx=−csc( )+k 1 Ex: ∫ cos(3x)dx= 3in (3x)+k −1 ∫ sinax+b )dx= co(ax+b +k a 1 ∫ cos(ax+b)dx= sin (ax+b)+k a Exponextial Fxnctions e dx=¿e +k ∫ ¿ ax+b 1 ax+b ∫ e dx= e +k a Antiderivatives and Differential Equations y=∫y' dx y=∫ mx+b dx 2 m x y= 2 +bx+k Given y x)=¿ find k Ex: y =2x+4 given y(0)=1 y=∫2 x+4dx=x +4 x+k y0)=1=0+0+k∴k=1

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