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Showing if the improper integral is convergent or divergent

I’ll send pic of question and working
7F381BD5-F611-4478-BDB4-1D89AEEAD804.png Question 14
Original post by InfinityMist
7F381BD5-F611-4478-BDB4-1D89AEEAD804.png Question 14

image.jpgI don’t get this line of working
Give me a sec boss
Original post by InfinityMist
image.jpgI don’t get this line of working

There are 3 lines there. Which don't you get?
Ok basically, if a is less than one, it's power will be positive therefore as t tends towards infinity it also tends towards infinity and therefore diverges. If a is greater than an 1, it tends towards 0 so you can get rid of that part of the equation after saying a is greater than 1. Therefore you're left with - (1/-a+1) which gets you the answer in the book, only when a is greater than one, which is the point it converges
Original post by CloutMaster
Ok basically, if a is less than one, it's power will be positive therefore as t tends towards infinity it also tends towards infinity and therefore diverges. If a is greater than an 1, it tends towards 0 so you can get rid of that part of the equation after saying a is greater than 1. Therefore you're left with - (1/-a+1) which gets you the answer in the book, only when a is greater than one, which is the point it converges

I forgot to mention, when a is greater than 1 it tends to 0 because t would be raised to a negative power. eg, 1/infinity tends towards 0. That's why you can get rid of that bit of the integral after stating the range of a
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davros
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Original post by CloutMaster
I forgot to mention, when a is greater than 1 it tends to 0 because t would be raised to a negative power. eg, 1/infinity tends towards 0. That's why you can get rid of that bit of the integral after stating the range of a

Please don't say "1/infinity tends towards 0". That makes my head hurt :biggrin:
Original post by InfinityMist
I’ll send pic of question and working

ops?
Original post by KaziMahathir
ops?

2 digits. 6.2
Original post by InfinityMist
2 digits. 6.2

BRO! You didn't have to do it!

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