# Calculus 1 : How to find trapezoidal approximation by graphing functions

## Example Questions

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### Example Question #1 : How To Find Trapezoidal Approximation By Graphing Functions

Use the trapezoidal approximation to find the area under the curve using the graph with four partitions.      Explanation:

The trapezoid rule states that .

Therefore, using our graph, we have: We find the function values at the sample point: Then we substitute the appropriate values into the trapezoid rule approximation: ### Example Question #2 : Trapezoidal Approximation

Is the following function increasing or decreasing at the point ? h(x) is increasing at , because the first derivative is positive.

h(x) is increasing at , because the second derivative is positive.

h(x) is decreasing at , because the first derivative is negative.

h(x) is decreasing at , because the second derivative is negative.

h(x) is decreasing at , because the first derivative is negative.

Explanation:

Is the following function increasing or decreasing at the point ? Increasing and decreasing intervals can be found via the first derivative. Since derivatives measure rates of change, the sign of the derivative at a given point can tell you whether a function is increasing or decreasing.

Begin by taking the derivative of our function: Becomes: Next, find h'(-6) and look at the sign. So, our first derivative is very negative at the given point. This means that h(x) is decreasing.

### Example Question #3 : Trapezoidal Approximation

Use the trapezoidal approximation to approximate the following integral:      Explanation:

The trapezoidal approximation of a definite integral is given by the following formula: Using the above formula, we get ### Example Question #4 : Trapezoidal Approximation

Use the trapezoidal approximation to evaluate the following integral:      Explanation:

To evaluate a definite integral using the trapezoidal approximation, we must use the formula Using the above formula, we get ### Example Question #5 : Trapezoidal Approximation

Use the trapezoidal approximation to evaluate the following integral:       Explanation:

To evaluate a definite integral using the trapezoidal approximation, we must use the formula Using the above formula, we get ### Example Question #6 : Trapezoidal Approximation

Evaluate the following integral using the trapezoidal approximation:       Explanation:

To evaluate the integral using the trapezoidal rule, we must use the formula Using the above formula, we get the following: ### Example Question #7 : Trapezoidal Approximation

Evaluate the integral using the trapezoidal approximation:      Explanation:

To evaluate a definite integral using the trapezoidal approximation, we must use the following formula: So, using the above formula, we get which simplifies to ### Example Question #8 : Trapezoidal Approximation

Evaluate the integral using the trapezoidal approximation:       Explanation:

To evaluate the definite integral using the trapezoidal approximation, we must use the following formula: Using the above formula, we get ### Example Question #9 : Trapezoidal Approximation

Evaluate the integral using the trapezoidal approximation:      Explanation:

To evaluate the integral using the trapezoidal approximation, we must use the following formula: Using the formula, we get ### Example Question #10 : Trapezoidal Approximation

Evaluate the integral using the trapezoidal approximation:       Explanation:

To evaluate the definite integral using the trapezoidal approximation, the following formula is used: Using the above formula, we get .

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