Finding a Pattern (a) Find ∫ cos 3 x d x (b) Find ∫ cos 5 x d x (c) Find ∫ cos 7 x d x (d) Explain how to find ∫ cos 15 x d x without actually integrating.
Finding a Pattern (a) Find ∫ cos 3 x d x (b) Find ∫ cos 5 x d x (c) Find ∫ cos 7 x d x (d) Explain how to find ∫ cos 15 x d x without actually integrating.
(d) Explain how to find
∫
cos
15
x
d
x
without actually integrating.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Is the function f(x) continuous at x = 1?
(z)
6
5
4
3.
2
1
0
-10
-9
-7
-5
-2
-1 0
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
Select the correct answer below:
○ The function f(x) is continuous at x = 1.
○ The right limit does not equal the left limit. Therefore, the function is not continuous.
○ The function f(x) is discontinuous at x = 1.
○ We cannot tell if the function is continuous or discontinuous.
Is the function f(x) shown in the graph below continuous at x = −5?
f(x)
7
6
5
4
2
1
0
-10
-9
-8 -7
-6
-5
-4
-3
-2
-1 0
1
2
3
4
5
6 7 8 9
10
-1
-2
-3
-4
-5
-6
-7
Select the correct answer below:
The function f(x) is continuous.
○ The right limit exists. Therefore, the function is continuous.
The left limit exists. Therefore, the function is continuous.
The function f(x) is discontinuous.
○ We cannot tell if the function is continuous or discontinuous.
4. Evaluate the following integrals. Show your work.
a)
-x
b) f₁²x²/2 + x² dx
c) fe³xdx
d) [2 cos(5x) dx
e) √
35x6
3+5x7
dx
3
g) reve
√ dt
h) fx (x-5) 10 dx
dt
1+12
Chapter 8 Solutions
Bundle: Calculus: Early Transcendental Functions, Loose-leaf Version, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus: Early Transcendental Functions, 6th Edition, Multi-Term
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