# How do you evaluate the definite integral #int (2x^-1) dx# from #[1,3.5]#?

The answer is

We use

So, our integral

By signing up, you agree to our Terms of Service and Privacy Policy

To evaluate the definite integral ( \int_{1}^{3.5} \frac{2}{x} , dx ), you need to find the antiderivative of ( \frac{2}{x} ), which is ( 2 \ln|x| ). Then, you evaluate this antiderivative at the upper and lower limits of integration and subtract the result obtained at the lower limit from the result obtained at the upper limit.

( \int_{1}^{3.5} \frac{2}{x} , dx = [2 \ln|x|]_{1}^{3.5} )

Substituting the upper and lower limits:

( = 2 \ln|3.5| - 2 \ln|1| )

Since ( \ln|1| = 0 ), the expression simplifies to:

( = 2 \ln|3.5| )

Now, you can compute the value of ( \ln|3.5| ) using a calculator:

( \approx 2 \cdot 1.252 )

( \approx 2.504 )

So, ( \int_{1}^{3.5} \frac{2}{x} , dx \approx 2.504 ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

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.

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.

- How do you integrate #tanx / (secx + cosx)#?
- How do you find the integral of #(1 + e^2x) ^(1/2)#?
- Evaluate the following definite integral to three significant digits. I have been using rule #int ((du)/u) = ln |u| + C # And come out with an answer of 0.546. The answer is 0.732?
- How do you find the derivative of #F(x)=int ln(t+1)dt# from #[0, e^(2x)]#?
- How do you evaluate the definite integral #int (4t^3-2t)dt# from [-1,1]?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7