Matched Problem 3 Referring to the figure for Example 3, calculate the definite integral (A) ∫ a 0 f ( x ) d x (B) ∫ 0 c f ( x ) d x (C) ∫ 0 b f ( x ) d x EXAMPLE 3 Definite Integrals Calculate the definite integrals by referring to Figure 9. (A) ∫ a b f ( x ) d x (B) ∫ a c f ( x ) d x (C) ∫ b c f ( x ) d x
Matched Problem 3 Referring to the figure for Example 3, calculate the definite integral (A) ∫ a 0 f ( x ) d x (B) ∫ 0 c f ( x ) d x (C) ∫ 0 b f ( x ) d x EXAMPLE 3 Definite Integrals Calculate the definite integrals by referring to Figure 9. (A) ∫ a b f ( x ) d x (B) ∫ a c f ( x ) d x (C) ∫ b c f ( x ) d x
Solution Summary: The above integral indicates the sum of area of the region A, from a to 0. The regions A lies in third quadrant with its area 2.33.
Matched Problem 3 Referring to the figure for Example 3, calculate the definite integral
(A)
∫
a
0
f
(
x
)
d
x
(B)
∫
0
c
f
(
x
)
d
x
(C)
∫
0
b
f
(
x
)
d
x
EXAMPLE 3 Definite Integrals Calculate the definite integrals by referring to Figure 9.
(A)
∫
a
b
f
(
x
)
d
x
(B)
∫
a
c
f
(
x
)
d
x
(C)
∫
b
c
f
(
x
)
d
x
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.
Students were asked to simplify the expression (secØ - cosØ)/secØ Two students' work is given.Student A: step 1 secØ/secØ - cosØ/secØstep 2 cosØ/1 - (1/cosØ)step 3 1 - cos^2Østep 4 sin^2ØStudent B: step 1 (1/cosØ)-cosØ)/secØstep 2 (1 - cos^2Ø/cosØ)/secØstep 3 sin^2Ø/cos^2Østep 4 tan^2ØPart A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused.Part B: Complete the student's solution correctly, beginning with the location of the error.
Although 330° is a special angle on the unit circle, Amar wanted to determine its coordinates using the sum and difference formulas.Part A: Determine cos 330° using the cosine sum identity. Be sure to include all necessary work.Part B: Determine sin 330° using the sine difference identity. Be sure to include all necessary work.
A public health researcher is studying the impacts of nudge marketing techniques on shoppers vegetables
Chapter 5 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
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