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How do you find the definite integral of #dx/ (x+2)# from #[0, 7]#?

Answer 1

Emily Ammerman

#2ln(3)-ln(2)#

Using that #int 1/xdx=ln|x|+C# we get

#int_0^7dx/(x+2)=[ln|x+2|]_0^7=ln(9)-ln(2)=2ln(3)-ln(2)#

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Answer 2

Emma Aldridge

To find the definite integral of ( \frac{dx}{x+2} ) from ( x = 0 ) to ( x = 7 ), you can use the formula for the natural logarithm function. The integral of ( \frac{1}{x+2} ) is ( \ln|x+2| ). Therefore, integrating ( \frac{dx}{x+2} ) from ( x = 0 ) to ( x = 7 ) yields ( \ln|7+2| - \ln|0+2| ). Simplifying, this becomes ( \ln(9) - \ln(2) ), which equals ( \ln\left(\frac{9}{2}\right) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.