# How do you use the Midpoint Rule with #n=5# to approximate the integral #int_1^(2)1/xdx# ?

The midpoints of the above subintervals are

Using the above midpoints to determine the heights of the approximating rectangles, we have

By Midpoint Rule,

I hope that this was helpful.

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

To approximate the integral ( \int_1^2 \frac{1}{x} , dx ) using the Midpoint Rule with ( n = 5 ), divide the interval ( [1, 2] ) into ( n = 5 ) subintervals of equal width. Then, find the midpoint of each subinterval and evaluate the function at these midpoints. Finally, multiply each function value by the width of the subintervals and sum them up to get the approximation of the integral.

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 area using the trapezoidal approximation method, given #cos(4 x) dx#, on the interval [-1, 2] with n=10?
- How do you use the trapezoidal rule with n=10 to approximate the area between the curve #1/sqrt(1+x^3)# from 0 to 2?
- How do you calculate the left and right Riemann sum for the given function over the interval [0, ln2], using n=40 for #e^x#?
- How do you use the trapezoidal rule with n=4 to approximate the area between the curve #sqrt(x) sinx# from pi/2 to pi?
- How do you find the Riemann sum associated with #f(x)=3x^2 +6#, n=3 and the partition of [0,6]?

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