题目
MAT136H5 S 2025 - All Sections 3.2 Preparation Check
多重下拉选择题
Problem: Evaluate the integral∫cos(4x)cos(7x)dx. Step-by-step solution: a) Look at the Rule above Example 3.13 in the textbook Links to an external site. . To evaluate the integral ∫cos(7x)cos(4x)dx should we use equation (3.3), (3.4) or (3.5)? [ Select ] Equation (3.5) Equation (3.4) Equation (3.3) b) In this example, a=7 and b=4. Which of the following options is correct? [ Select ] Option I Option III Option II Option I: ∫cos(7x)cos(4x)dx=∫( 1 2 cos(3x)− 1 2 cos(11x))dx Option II: ∫cos(7x)cos(4x)dx=∫( 1 2 cos(3x)+ 1 2 cos(11x))dx Option III: ∫cos(7x)cos(4x)dx=∫( 1 2 cos(11x)+ 1 2 cos(7x))dx c) Now integrate your answer from (b). Which is the correct final answer to the problem? Option C Option A: ∫cos(7x)cos(4x)dx= 1 6 sin(3x)− 1 22 sin(11x)+C Option B: ∫cos(7x)cos(4x)dx= 1 22 sin(11x)+ 1 14 sin(7x)+C Option C: ∫cos(7x)cos(4x)dx= 1 6 sin(3x)+ 1 22 sin(11x)+C Option D: ∫cos(7x)cos(4x)dx=− 3 2 sin(3x)− 11 2 sin(11x)+C
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思路分析
Question restatement:
- Problem: Evaluate the integral ∫ cos(4x) cos(7x) dx. The problem is presented in parts:
a) Which equation (3.3), (3.4), or (3.5) should be used to evaluate ∫ cos(7x) cos(4x) dx?
b) In this example, a = 7 and b = 4. Which option is correct: I, II, or III? And what is the expansion for ∫ cos(7x) cos(4x) dx?
c) Now integrate the chosen expression from (b) to obtain the final answer, selecting among A, B, C, or D.
- Answer key provided: ["Equation (3.5)", "Option II", "Option C"]
- Answer options (for reference in the explanation):
a) Equation (3.5)
Equation (3.4)
Equation (3.3)
b) Option I
Option III
Option II
c) Option A
Option B
Option C
Option D
Analysis of each op......Login to view full explanation登录即可查看完整答案
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