How do you evaluate the integral #int 1/(2x1)# from 1 to 2?
I found:
Try this:
By signing up, you agree to our Terms of Service and Privacy Policy
To evaluate the integral (\int_{1}^{2} \frac{1}{2x1} , dx):

Perform a substitution: Let ( u = 2x  1 ). Then, ( du = 2 , dx ) or ( \frac{1}{2} du = dx ).

Substitute the limits of integration: When ( x = 1 ), ( u = 2(1)  1 = 1 ). When ( x = 2 ), ( u = 2(2)  1 = 3 ).

Rewrite the integral in terms of ( u ): [ \int \frac{1}{u} \cdot \frac{1}{2} , du ]

Integrate: [ \frac{1}{2} \int \frac{1}{u} , du = \frac{1}{2} \lnu + C ] Where ( C ) is the constant of integration.

Substitute back for ( u ): [ \frac{1}{2} \ln2x1 ]

Evaluate from 1 to 2: [ \frac{1}{2} \ln2(2)1  \frac{1}{2} \ln2(1)1 ] [ = \frac{1}{2} \ln(3)  \frac{1}{2} \ln(1) ] [ = \frac{1}{2} \ln(3) ]
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
 How do you find the indefinite integral of #int (7/sqrt(1u^2))du#?
 How do you use the limit process to find the area of the region between the graph #y=16x^2# and the xaxis over the interval [1,3]?
 How do you find the indefinite integral of #int 5^x#?
 What is the integral of #int (2xsinx) / (x^2 + cosx)#?
 How do you integrate #int x (3x+1)^10 # ?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7