# How do you do the trapezoidal rule to compute #int logxdx# from [1,2]?

It's important to notice that it's only an approximate value (n=1) and it contain a percentage of error : the correct value would be around 0.38629, but with this formula we found approximately 0.34657.

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

To use the trapezoidal rule to approximate the integral of ( \log(x) ) from 1 to 2, follow these steps:

- Divide the interval ([1, 2]) into ( n ) subintervals of equal width. Let ( n ) be the desired number of subintervals.
- Calculate the width of each subinterval, ( \Delta x ), using the formula: ( \Delta x = \frac{b - a}{n} ), where ( a = 1 ) and ( b = 2 ).
- Evaluate the function ( \log(x) ) at the endpoints of each subinterval and sum the values.
- Multiply the sum by ( \Delta x ).
- Adjust the result by subtracting half the first term and half the last term.

The formula for the trapezoidal rule is:

[ \text{Trapezoidal Rule} = \Delta x \left( \frac{1}{2}f(a) + f(x_1) + f(x_2) + \cdots + f(x_{n-1}) + \frac{1}{2}f(b) \right) ]

Where ( x_1, x_2, \ldots, x_{n-1} ) are the interior points of the subintervals.

Substitute ( a = 1 ), ( b = 2 ), and ( f(x) = \log(x) ) into the formula, along with the calculated ( \Delta x ), and compute the result.

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 Use Simpson's rule with #n=8# to approximate the integral #int_0^pix^2*sin(x)dx#?
- How do you approximate the area under #y=10−x^2# on the interval [1, 3] using 4 subintervals and midpoints?
- How do you write the Simpson’s rule and Trapezoid rule approximations to the #intsinx/x# over the inteval [0,1] with #n=6#?
- How do you use n = 5 equally divided subdivisions to estimate the integral from 1 to 3 of #(1/x^2)dx# with the right-hand Riemann sum?
- Determine a region whose area is equal to the given limit?

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