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Week 1 Notes Calc II

by: Jared Hopland

Week 1 Notes Calc II MATH 142 001

Marketplace > UTK > Applied Mathematics > MATH 142 001 > Week 1 Notes Calc II
Jared Hopland
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About this Document

Covers Antiderivative, Power Rule, Linearity Rule, Antiderivative of Trig Functions, Antiderivative of Exponential Functions, And Antiderivatives with Differential Equations.
Calculus II
Dr. Stephenson
Class Notes
Math, Calc, Calculus, Calc II, Calc 2, utk, University of Tennessee, University Tennessee, University of Tennessee Knoxville




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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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