Questions
Single choice
The exact value of \( \int_{0}^{\pi }{(-2\cos} \frac{x}{3} )dx \) is:
View Explanation
Verified Answer
Please login to view
Step-by-Step Analysis
We start by restating the problem: evaluate the definite integral ∫ from 0 to π of (-2 cos(x/3)) dx, and identify the correct option among the provided choices.
First, perform the antiderivative. The integrand is -2 cos(x/3). Let u = x/3, so d......Login to view full explanationLog in for full answers
We've collected over 50,000 authentic exam questions and detailed explanations from around the globe. Log in now and get instant access to the answers!
Similar Questions
Question textThe definite integral\displaystyle \int_0^{\frac{\pi}{2}} \sin^4(x)\cos^3(x)\,dx can be evaluated using the trigonometric identity\sin^2(x) + \cos^2(x)=1and then use of integration by substitution. This gives\displaystyle \int_0^{\frac{\pi}{2}} \sin^4(x)\cos^3(x)\,dx = \displaystyle \int_0^1 u^a - u^b\, du where a and b are positive integers.The final solution is of the form \dfrac{2}{A} where A is an integer.Fill in the correct values for a,\,\,b and A.a = Answer 1 Question 29[input] b = Answer 2 Question 29[input] A = Answer 3 Question 29[input]
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
Find the average value of the function f(x)=sin6(x)cos3(x) over interval [−π,π]
Evaluate ∫ sec 3 ( 𝜃 ) tan 5 ( 𝜃 ) 𝑑 𝜃 .
More Practical Tools for Students Powered by AI Study Helper
Making Your Study Simpler
Join us and instantly unlock extensive past papers & exclusive solutions to get a head start on your studies!