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