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How do you integrate #10^x dx# from 1 to 0?

Answer 1

I would do, using fundamental integration/derivation techniques, like this (from #1# to #0#): #int_1^0(10^x)dx=10^x/ln(10)|_1^0=1/ln(10)-10/ln(10)=-9/ln(10)#

Hope it helps!

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Answer 2

Adam Adkins

To integrate (10^x , dx) from (1) to (0), you use the definite integral formula:

[ \int_{a}^{b} 10^x , dx = \left[ \frac{10^x}{\ln(10)} \right]_{a}^{b} ]

Plugging in the values (a = 1) and (b = 0), you get:

[ \left[ \frac{10^x}{\ln(10)} \right]_{1}^{0} ]

Now, evaluate the expression at (x = 0) and subtract the value at (x = 1):

[ \frac{10^0}{\ln(10)} - \frac{10^1}{\ln(10)} ]

[ = \frac{1}{\ln(10)} - \frac{10}{\ln(10)} ]

[ = \frac{1 - 10}{\ln(10)} ]

[ = \frac{-9}{\ln(10)} ]

So, the definite integral of (10^x , dx) from (1) to (0) is (\frac{-9}{\ln(10)}).

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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.