### All AP Calculus BC Resources

## Example Questions

### Example Question #7 : Riemann Sums

Given a function , find the Right Riemann Sum of the function on the interval divided into four sub-intervals.

**Possible Answers:**

**Correct answer:**

In order to find the Riemann Sum of a given function, we need to approximate the area under the line or curve resulting from the function using rectangles spaced along equal sub-intervals of a given interval. Since we have an interval divided into sub-intervals, we'll be using rectangles with vertices at .

To approximate the area under the curve, we need to find the areas of each rectangle in the sub-intervals. We already know the width or base of each rectangle is because the rectangles are spaced unit apart. Since we're looking for the Right Riemann Sum of , we want to find the heights of each rectangle by taking the values of each rightmost function value on each sub-interval, as follows:

Putting it all together, the Right Riemann Sum is

.

### Example Question #1 : Riemann Sum: Right Evaluation

**Possible Answers:**

**Correct answer:**

### Example Question #2 : Riemann Sum: Right Evaluation

**Possible Answers:**

**Correct answer:**

### Example Question #3 : Riemann Sum: Right Evaluation

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Riemann Sum: Right Evaluation

**Possible Answers:**

**Correct answer:**

### Example Question #21 : Integrals

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Riemann Sum: Right Evaluation

**Possible Answers:**

**Correct answer:**

### Example Question #7 : Riemann Sum: Right Evaluation

**Possible Answers:**

**Correct answer:**

### Example Question #8 : Riemann Sum: Right Evaluation

**Possible Answers:**

**Correct answer:**

### Example Question #21 : Numerical Approximations To Definite Integrals

**Possible Answers:**

**Correct answer:**

Certified Tutor

Certified Tutor