Questions
MAT137Y1 LEC 20249: Calculus with Proofs (all lecture sections) Pre-Class Quiz 46 (9.7,9.8 and 9.9)
Single choice
Evaluate ∫ sec 3 ( 𝜃 ) tan 5 ( 𝜃 ) 𝑑 𝜃 .
Options
A.1
5
sec
5
(
𝜃
)
−
1
3
sec
3
(
𝜃
)
+
𝐶
B.1
7
sec
7
(
𝜃
)
−
2
5
sec
5
(
𝜃
)
+
1
3
sec
3
(
𝜃
)
+
𝐶
C.1
7
sec
7
(
𝜃
)
−
1
5
sec
5
(
𝜃
)
+
𝐶
D.1
3
sec
3
(
𝜃
)
−
1
5
sec
5
(
𝜃
)
+
𝐶
E.1
7
sec
7
(
𝜃
)
−
1
3
sec
3
(
𝜃
)
+
𝐶
View Explanation
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Step-by-Step Analysis
To evaluate the integral ∫ sec^3(θ) tan^5(θ) dθ, I will work by expressing everything in terms of sec(θ) and d(sec θ).
Option A: (1/5) sec^5(θ) − (1/3) sec^3(θ) + C. This attempt suggests integrating to lower powers of sec, but differentiating these terms would produce derivatives involving tan(θ) sec^3(θ) or similar forms, not matching the original integrand structure. In short, this pattern do......Login to view full explanationLog in for full answers
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