the fundamental theorem of calculus (ex 11e )...question 1 a. find the exact value of the definite...

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 )

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

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

Question 8

Question 9