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Calc 5.4b
 

Calc 5.4b

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    Calc 5.4b Calc 5.4b Presentation Transcript

    • 5.4b Exponential Functions: Integration Integrate natural exponential functions
    • Each of the rules for derivatives of exponential functions has a correlating integration rule. With e u you just need a matching du and you can put the chain back in the box!
    • Ex 7. p354 Integrating Exponential Functions Find Let u = 5x-1. Then du = 5dx. So I need a factor of 5 on the inside, and 1/5 on the outside. Back-substitute
    • Recall that you can multiply in constants, but cannot do that with missing variables that you might need. Ex 8 p. 354 Integrating Exponential Functions Find Rewrite to fit needs of du.
    • Ex 9 p. 355 Integrating Exponential Functions
    • Ex. 10 p. 355 Finding areas bounded by exponential functions Evaluate each definite integral. To get exact answers, you might need to evaluate by hand.
    • Ex 10 p. 355 Remember natural log rule where numerator is derivative of denominator!
    • Ex 10 p. 355 Use radian mode unless you know for sure angles are in degrees!
    • 5.4b p. 356/ 79, 85-109 odd 113-115, 120