# How do you evaluate the definite integral #int (1/2x-1) dx# from #[0, 3]#?

The answer is

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

To evaluate the definite integral (\int_{0}^{3} \frac{1}{2x-1} , dx), you first need to find the antiderivative of (\frac{1}{2x-1}), which is (\frac{1}{2} \ln|2x-1|). Then, you evaluate this antiderivative at the upper and lower limits of integration and subtract the lower value from the upper value.

So, evaluate (\frac{1}{2} \ln|2x-1|) at (x = 3) and (x = 0), then subtract the result of the evaluation at (x = 0) from the result of the evaluation at (x = 3).

[ \int_{0}^{3} \frac{1}{2x-1} , dx = \left[\frac{1}{2} \ln|2x-1|\right]_{0}^{3} = \frac{1}{2} \ln|2(3)-1| - \frac{1}{2} \ln|2(0)-1| ]

[ = \frac{1}{2} \ln|6-1| - \frac{1}{2} \ln|-1| = \frac{1}{2} \ln(5) - \frac{1}{2} \ln(1) = \frac{1}{2} \ln(5) - \frac{1}{2} \cdot 0 = \frac{1}{2} \ln(5) ]

So, (\int_{0}^{3} \frac{1}{2x-1} , dx = \frac{1}{2} \ln(5)).

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 find the indefinite integral of #int (x+1/x)^2dx#?
- How do you find the integral of #int (1 + cos x)^2 dx#?
- How do you evaluate the definite integral #int x^2 dx# from #[0,1]#?
- Let I= integral 1 to 0 9÷(3+x^2)^2 dx (i) Using the substitution x=(root 3) tan theta, show that I= (root 3) Integral 1÷6pie to 0 cos^2 theta dtheta. (ii) Hence find the exact value of I Can someone please solve this question?
- Help me please? with indefinite integral ln(cosx)dx/cos^2x

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