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Question 1
a. Find the exact value of the definite integral:
b. Confirm your answer above using CAS.
c. Will this definite integral represent the area under the graph between 𝑥 = −𝜋
6 to
𝑥 =𝜋
6 ? Explain your answer.
Question 2
a. Evaluate the definite integral:
b. Confirm your answer by evaluating this definite integral on CAS.
c. Can this definite integral be interpreted as the area under the graph of 𝑦 = sin (2𝑥 −𝜋
3) ?
Explain your answer. (Hint: Draw a graph)
The Fundamental Theorem of Calculus (Ex 11E )
![Page 2: The Fundamental Theorem of Calculus (Ex 11E )...Question 1 a. Find the exact value of the definite integral: b. Confirm your answer above using CAS. c. Will this definite integral](https://reader034.vdocuments.mx/reader034/viewer/2022051804/5fefe087fff9e7155d14bfbb/html5/thumbnails/2.jpg)
Question 3
Question 4
a. Evaluate the definite integral ∫ (2𝑒𝑥
33
0+ 5)𝑑𝑥
b. Draw a suitable graph that illustrates the meaning of this definite integral as the
area under a graph.
Question 5
a. Evaluate the definite integral: ∫4
𝑥−6+ 2 𝑑𝑥
10
7
![Page 3: The Fundamental Theorem of Calculus (Ex 11E )...Question 1 a. Find the exact value of the definite integral: b. Confirm your answer above using CAS. c. Will this definite integral](https://reader034.vdocuments.mx/reader034/viewer/2022051804/5fefe087fff9e7155d14bfbb/html5/thumbnails/3.jpg)
b. Sketch a graph and interpret this definite integral as the area under a graph and
the vertical lines: 𝑥 = 7 and 𝑥 = 10.
Question 6
a. Evaluate the definite integral: ∫1
√𝑥−3− 1 𝑑𝑥
7
325
36
b. Explain why the value of this definite integral is said to represent a signed area.
Question 7
![Page 4: The Fundamental Theorem of Calculus (Ex 11E )...Question 1 a. Find the exact value of the definite integral: b. Confirm your answer above using CAS. c. Will this definite integral](https://reader034.vdocuments.mx/reader034/viewer/2022051804/5fefe087fff9e7155d14bfbb/html5/thumbnails/4.jpg)
Question 8
Question 9