Trapezoidal Rule

The table provides a person's cholesterol level at selected times during a 10-week treatment period.

What is the average cholesterol level over the 10-week period, approximated by a trapezoidal sum with the subintervals [0, 2], [2, 6], and [6, 10]?

Which of the following statements best describes the primary difference in the calculation of a midpoint Riemann sum and a trapezoidal sum?

What is a primary advantage of approximating a definite integral with a trapezoidal sum instead of a left or right Riemann sum?

All of the following statements concerning trapezoidal sums are true EXCEPT:

The table above shows selected values for a function $$f$$ that is continuous on the closed interval $$[0, 6]$$. If the trapezoidal approximation of $$\displaystyle \int_{0}^{6} f(x) dx$$ using three subintervals of equal length is 52, what is the value of $$k$$?

Which of the following methods approximates the area under a curve using a collection of trapezoids?

The trapezoidal rule applied to a function f on the subintervals [0, 2] and [2, 4] yields an area of 28, as represented by the equation below. What is the value of f(2)?

$$\frac{1}{2}(3+f(2))(2-0) + \frac{1}{2}(f(2)+11)(4-2)=28$$

The equation $$\frac{1}{2}(H(2)+H(3))(3-2) = 3.25$$ represents the approximation of an integral using a single trapezoid. If $$H(2) = 1.5$$, what is the value of $$H(3)$$?

Using the graph of $$f(x)=\ln(x)$$ on the interval $$[1,4]$$, approximate the definite integral $$\int_{1}^{4} \ln(x) dx$$ by applying the trapezoidal rule with 3 equal subintervals.

Using the trapezoidal rule with $$n=2$$, which of the following is an approximation for $$\int_{1}^{3} \ln(x) dx$$?

The magnitude of the error in a trapezoidal rule approximation is determined for `n = 10, 20, 40,` and `80` subintervals. Which of the following lists these values of `n` in order from the one that yields the largest error to the one that yields the smallest error?

The table shows values for a function $$f$$ at selected times $$t$$. Which of the following expressions gives the trapezoidal approximation of $$\int_{0}^{6} f(t) dt$$ using the three subintervals indicated by the table?

The table below gives selected values for a continuous function $$f$$.

Using the trapezoidal rule with the five subintervals indicated by the table, what is the approximate value of $$\int_{0}^{5} f(x) dx$$?

Using the graph of $$f(x)=\cos(x)$$ on the interval $$[0,\frac{\pi}{2}]$$, approximate the area under the curve using the trapezoidal rule with 2 subintervals.

Based on the graph above representing $$f(x)=x^2$$, which of the following is true regarding the trapezoidal approximation of the area under the curve on the interval from $$x=1$$ to $$x=3$$ using a single trapezoid?

The table above shows selected values for a function H. Use a trapezoidal sum with the subintervals indicated by the data to approximate the area under the curve of H from t = 2 to t = 10.

The error in the trapezoidal rule approximation of $\displaystyle\int_{0}^{1}$ eˣ dx with n = 4 subintervals is most nearly:

The table shows values for a function `H(t)`. Which of the following correctly orders the steps for approximating the area under the curve of `H` using a trapezoidal sum with the subintervals indicated by the table?

The area under the curve $$y=3x^2$$ on the interval $$[0, 2]$$ is approximated using a trapezoidal sum with two subintervals of equal width. What is the value of this approximation?

What is the trapezoidal sum approximation for $$\int_{1}^{6} (2x - 1) dx$$ using five equal subintervals?

Use a trapezoidal sum with two subintervals indicated by the table to approximate the value of $$\int_{0}^{4} f(x) dx$$.

The table shows values of a function `f` for selected values of `x`. Which of the following expressions represents the trapezoidal sum approximation of $$\int_{0}^{7} f(x) dx$$?

The table below provides selected values for a function $H(t)$. Using a trapezoidal sum with the four subintervals indicated by the table, what is the approximation of $$\int_{2}^{10} H(t) dt$$?

The table provides selected values for a function `H`. Use a trapezoidal sum with the subintervals indicated in the table to approximate $$\int_{2}^{10} H(t) dt$$.

In a trapezoidal Riemann sum, how is the area of a single trapezoid calculated?

The table below gives selected values for a function $H$. Which of the following shows the correct calculation for a trapezoidal sum approximation of $$\int_{2}^{10} H(t) dt$$?

The table shows values for a function H at selected values of t. Which of the following is true about the trapezoidal approximation of $$ \int_{2}^{10} H(t) dt $$ using the subintervals given by the data in the table?

| Years (t) | 2 | 3 | 5 | 7 | 10 |
| Height (H(t)) | 1.5 | 2 | 6 | 11 | 15 |

The table provides selected values for a function $$H$$. Using a trapezoidal sum with the subintervals indicated by the table, which of the following expressions approximates $$\int_{2}^{10} H(t) dt$$?

The table below provides values for a function H at selected times t.

Which of the following expressions gives the trapezoidal approximation of the integral of H(t) from t=2 to t=10, using the subintervals indicated by the data in the table?

I.

$$\frac{1}{2}*(1.5+2)*1 + \frac{1}{2}*(2+6)*2 + \frac{1}{2}*(6+11)*2 + \frac{1}{2}*(11+15)*3$$

II.

$$1*(1.5) + 2*(2) + 2*(6) + 3*(11)$$

III.

$$\frac{1}{2}*(2+6)*1 + \frac{1}{2}*(6+11)*2 + \frac{1}{2}*(11+15)*3$$

A table extracted from the graph provides the following values for a function $$H(t)$$:

Using the trapezoidal rule, estimate the definite integral of $$H(t)$$ with respect to t over the interval from 2 to 10.

The table provides selected values for a function `f`. Which of the following shows the correct computation for a trapezoidal sum approximation of $$\int_{0}^{6} f(x) dx$$ using the three subintervals indicated by the data?