# How do you Use the trapezoidal rule with #n=6# to approximate the integral #int_0^3dx/(1+x^2+x^4)dx#?

The trapezoidal rule is just a formula. From what we are given, we have:

The formula is:

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

To use the Trapezoidal Rule with ( n = 6 ) to approximate the integral ( \int_{0}^{3} \frac{dx}{1 + x^2 + x^4} ), you partition the interval ([0, 3]) into ( n = 6 ) subintervals of equal width. Then, you compute the function values at the endpoints of these subintervals and apply the Trapezoidal Rule formula:

[ \int_{a}^{b} f(x) , dx \approx \frac{h}{2} \left[ f(x_0) + 2f(x_1) + 2f(x_2) + \ldots + 2f(x_{n-1}) + f(x_n) \right] ]

where ( h ) is the width of each subinterval, ( a ) and ( b ) are the lower and upper limits of integration respectively, and ( x_0, x_1, \ldots, x_n ) are the partition points.

In this case, ( a = 0 ), ( b = 3 ), ( n = 6 ), and ( h = \frac{b - a}{n} = \frac{3 - 0}{6} = \frac{1}{2} ).

Then, compute the function values at the endpoints of the subintervals:

[ f(0), f(0.5), f(1), f(1.5), f(2), f(2.5), f(3) ]

Substitute these values into the Trapezoidal Rule formula and perform the computation to obtain the approximation for 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.

- Using Right Riemann Sums, approximate the area under the curve #5x^2-4x# in the interval #[0,3]# with #6# strips?
- How do you find the area between 1 and 2 of #(3x^2-2)dx# using reimann sums?
- How do you find the Riemann sum for #f(x) = x - 5 sin 2x# over 0 <x <3 with six terms, taking the sample points to be right endpoints?
- How do you use Riemann sums to evaluate the area under the curve of #f(x)= 3x # on the closed interval [1,5], with n=4 rectangles using right, left, and midpoints?
- How do you use Riemann sums to evaluate the area under the curve of #f(x)=x^3# on the closed interval [1,3], with n=4 rectangles using right, left, and midpoints?

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