$MathMaster logo$

MathMaster

Home
general
trigonometric function integral sen 2x cos 4x dx

Question

trigonometric function: integral sen(2x)cos(4x)dx

169

likes

846 views

Answer to a math question trigonometric function: integral sen(2x)cos(4x)dx

$Expert avatar$

4.5

91 Answers

$=\int \frac{\sin(2x+4x)+\sin(2x-4x)}{2}dx$

$=\frac{1}{2}\cdot \int \sin(2x+4x)+\sin(2x-4x)dx$

$=\frac{1}{2}(\int \sin(2x+4x)dx+\int \sin(2x-4x)dx)$

$=\frac{1}{2}(-\frac{1}{6}\cos(6x)+\frac{1}{2}\cos(2x))$

$=\frac{1}{2}(-\frac{1}{6}\cos(6x)+\frac{1}{2}\cos(2x))+C$

Frequently asked questions (FAQs)

Question: Convert 30 millimeters to centimeters.

+

Find the basis of vectors for the subspace spanned by (2, -1, 3) and (1, 0, -2).

+

What are the solutions to the quadratic equation 3x^2 - 5x + 2 = 0?

+

New questions in Mathematics

A pump with average discharge of 30L/second irrigate 100m wide and 100m length field area crop for 12 hours. What is an average depth of irrigation in mm unIt?

Solution of the equation y'' - y' -6y = 0

A book is between 400 and 450 pages. If we count them 2 at a time there is none left over, if we count them 5 at a time there is none left over and if we count them 7 at a time there are none left over, how many pages does the book have?

The random variable Y is defined as the sum between two different integers selected at random between -4 and 2 (both included). What are the possible values of the random variable Y? What is the value of P(Y=-3)? And whether it is less than or equal to -5?

5) A family with a father, mother and 3 children must sit on five chairs in a row and the only restriction is that the mother must be at one end. In how many different ways can they be seated?

The Lenovo company manufactures laptop computers, it is known that for every 60 laptops produced, 54 go on the market with the highest quality standards. If a sample of 15 laptops is taken, calculate the probability that: Exactly 2 are not of high quality

what is the annual rate on $525 at 0.046% per day for 3 months?

Determine the momentum of a 20 kg body traveling at 20 m/s.

∫ √9x + 1 dx

4x + 8y = 5 2x + 4y = 10

Primes are numbers divisible only by 1 and themselves; There are infinitely many prime numbers and the first ones are 2, 3, 5, 7, 11, 13, 17, 19, 23, .... Consider a 12-sided die, with the faces numbered from 1 to 12. Out of 4 rolls, the probability that only the first three numbers are primes is:

6-35 A recent study by an environmental watchdog determined that the amount of contaminants in Minnesota lakes (in parts per million) it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is a) Greater than 72 ppm. b) Between 64 and 72 ppm. c) Exactly 64 ppm. d) Greater than 94 ppm.

User The average height of Aranka, Böske, Cili, Delinke and Lili is 172 cm. We know that Aranka and Cili are both 172 cm tall. The sum of the heights of Böské and Delinke is 336 cm. How tall is Lili?

When taking a test with m closed answers, a student knows the correct answer with probability p, otherwise he chooses one of the possible answers at random. What is the probability that the student knows the correct answer given that he answered the question correctly.

A salesperson earns a base salary of $600 per month plus a commission of 10% of the sales she makes. You discover that on average, it takes you an hour and a half to make $100 worth of sales. How many hours will you have to work on average each month for your income to be $2000?

A post office has three categories of letters: 60% are from businesses, 30% are individual mail, and the remaining 10% are government mail. 5% of the letters from businesses have address errors, 10% of the individual mail has address errors, while 1% of the government mail has address errors. If we receive a letter with an address error, what is the probability that it is individual mail?"

Marc, Jean and Michelle have traveled a lot. Marc drove twice as much as Jean, but it was Michelle who drove the most with 100km more than Marc. They respected their objective of not exceeding 1350km of distance. How far did John drive?

A candy manufacturer must monitor deviations in the amount of sugar in their products They want their products to meet standards. They selected a random sample of 20 candies and found that the sandard deviation of that sample is 1.7. What is the probabilty of finding a sample variance as high or higher if the population variance is actually 3277 Assume the population distribution is normal.

A triangle is cut by a line s parallel to the base in such a way that it divides the side of the triangle into parts in the ratio of 2 : 3. Find the other side of the triangle if it is known that the line s divides it into parts whose length is 5 cm.