Introduction to the Definite Integral Lesson

​Introduction to the Definite Integral Lesson

​"Using Knowledge wisely will give you the Power to leap to tomorrow's edge."

By: Mr. C.

Multiple Choice

Using the areas of each region given
$$\int_a^cf\left(x\right)=$$  . #1

• 20

• -7

• -10

• -4

Multiple Choice

Using the areas of each region given
$$\int_a^df\left(x\right)=$$  #3

• 6

• 20

• 2

• 24

Fill in the Blank

The graph of $$y=-3x^2+12x-9$$ is shown. Find the area under the curve between x = 1, and x = 3. #48

Use the TI 84 Calculator.

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Multiple Choice

A Riemann Sum uses rectangles to...#18

• approximate the area under a curve. The more rectangles, the better the approximation.

• approximate the area under a curve. The less rectangles, the better the approximation.

• approximate the area under a curve. The more rectangles, the worse the approximation.

Multiple Choice

What is the meaning of the following symbol? #36

$$\int_a^bf\left(x\right)dx$$  

• The area from the curve to the x-axis from x = a to x = b

• The rate at which f(x) is changing from x = a to x = b

• The area from the curve to the y-axis from x = a to x = b

• The volume when the curve is rotated about the x-axis from x = a to x = b

Multiple Choice

Classify as an underestimate or overestimate. #11

• Underestimate

• Overestimate

Multiple Choice

For a function that is strictly increasing, a right hand Riemann Sum is which of the following: #30

• Overestimate
• Underestimate
• Unable to Determine
• Exact Solution

Multiple Choice

This is a velocity-time graph: What is the displacement of the object between 30 and 70 seconds? (area under curve) #43

• 800 m

• 600 m

• 400 m

• - 0.5 m

Multiple Choice

This graph shows the speed of a car during its first 6 seconds. How far did the car travel (displacement) during the last 2 seconds (4 - 6 s)? #45

• 10 m

• 20 m

• 10 m/s

• 20 m/s

Multiple Choice

Calculate the distance travelled in section C. #46

• 200 m

• 300 m

• 400 m

• 500 m

Left & right Riemann sums (article) | Khan Academy

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Multiple Choice

Is the graph using the Left, Right, or Midpoint Rule? #12

• left

• right

• midpoint

• none

Multiple Choice

Is the graph using Left, Right, or Midpoint Rule? #10

• left

• right

• midpoint

• none

Multiple Choice

What does this picture represent? #33

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

Multiple Choice

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.) #4

• 5(3) + 1(4) + 2(5) + 1(7)
• 5(4) + 1(5) + 2(7) + 1(6)
• 5(3) + 6(4) + 8(5) + 9(7)
• 0(3) + 5(4) + 6(5) + 8(7)

Multiple Choice

Find the right-hand Riemann Sum, with three sub-intervals indicated by the table. #5

• 28

• 16

• 34

• 21

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Multiple Choice

Calculate the approximation for the given function & interval. #6

R₃, f(x) = 7 - x, [3, 5]

• 16/3

• 5

• 26/3

• DNE

Multiple Choice

#15

• 1.5

• 1.1418

• 1.1

• 1.4914

Multiple Choice

#16

• 35

• 40.625

• 32.1

• 41

Multiple Choice

What is the approximate area of the region, using 4 subintervals and heights using left values? #23

• 7.5

• 7.75

• 10

• 11.5

Multiple Choice

Use a Midpoint Riemann Sum to approximate the area between 0 to 3 with 3 subintervals. #38

• 14

• 7

• 26

• 11

Multiple Choice

Find the area under the curve y =3x²-2x from x= 1 to x =5. Do not use your calculator. Use the Midpoint Rule with 4 subintervals for the graph shown. #39

• 100

• 99

• 150

• 152

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Multiple Choice

Based on the table, use a trapezoidal sum of 4 sub-intervals to estimate the area under the curve. #53

• 32.5

• 40.5

• 78

• 160

Multiple Choice

Use 3 trapezoids to determine the approximate area of the shaded area. #54

• 12

• 9

• 10

• 5