0
Best way: Use angle addition.
Sin(Ax)Cos(Bx) = (1/2) [sin[sum x] + sin[dif x]], where sum = A+B and dif = A-B
To show this,
Sin(Ax)Cos(Bx) = (1/2) [sin[(A+B) x] + sin[(A-B) x]]
= (1/2) [(sin[Ax]Cos[Bx]+sin[Bx]cos[Ax]) + (sin[Ax]cos[-Bx]+sin[-Bx]cos[Ax])]
Using the facts that cos[-k] = cos[k] and sin[-k] = -sin[k], we have:
(1/2) [(sin[Ax]Cos[Bx]+sin[Bx]cos[Ax]) + (sin[Ax]cos[-Bx]+sin[-Bx]cos[Ax])]
(1/2) [(sin[Ax]Cos[Bx]+sin[Bx]cos[Ax]) + (sin[Ax]cos[Bx]-sin[Bx]cos[Ax])]
(1/2) 2sin[Ax]Cos[Bx]
sin[Ax]Cos[Bx]
So,
Int[Sin(3y)Cos(5y)dy] = (1/2)Int[Sin(8y)-Sin(2y)dy]
= (-1/16) Cos[8y] +1/4 Cos[2y] + C
You would get the same result if you used integration by parts twice and played around with trig identities.
Add your answer:
Earn +20 pts
What is the indefinite integral of 3sinx-5cosx?
8
What is the convulusion integral?
Do you mean the Convolution Integral?
Integral of -x 2?
The integral of -x2 is -1/3 x3 .
What is the integral of 2 2x?
2 2x makes no sense. If you meant the integral of 2x, it is x2 + C. If you meant the integral of 4x, it is 2x2 + C. If you meant the integral of 2x2, it is 2/3 x3 + C.
What is the difference between Riemann and Lebesgue integral?
The Lebesgue integral covers a wider variety of cases. Specifically, the definition of hte Riemann integral permits a finite number of discontinuities; the Lebesgue integral permits a countable infinity of discontinuities.
What is the indefinite integral of 3sinx-5cosx?
8
Integral in tagalog?
Integral in Tagalog: mahalaga
How is Riemann- stieltjes integral a generalization of Riemann integral?
In reimann stieltjes integral if we assume a(x) = x then it becomes reimann integral so we can say R-S integral is generalized form of reimann integral.
How do you put the word integral in a sentence?
What is a integral
What is the convulusion integral?
Do you mean the Convolution Integral?
Sentence for integral?
Elections are integral to democracies.
What is integral number?
non integral is type of numbers behaviour: i can say that set of numbers without any "holes inside" are integral and set of numbers with "holes inside are non integral. example : integral group "1..100" non integral group "1,4,8,67"
What are some sentences with the word integral?
Political parties are an integral part of democracy. Religion is an integral part of Saudi Arabia. Greed is an integral part of human psychology.
State the difference between particular solution and particular integral?
Particular integral is finding what the integral is for example the integral of 2x is x^2 + C. Finding the particular solution would be finding what C equals from the particular integral.
How calculate the double integral?
First we have to evaluate the inner integral using ILATE method and then evaluate the outer integral
When was Integral Systems created?
Integral Systems was created in 1982.
What is the population of Integral Systems?
Integral Systems's population is 769.
