- #1
teng125
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may i know how to integ (sin x^4) ??
the answer is 1/32(12x - 8sin 2x + sin4x)
the answer is 1/32(12x - 8sin 2x + sin4x)
Again, you can use Power-reduction formulas. Then use some Product-to-sum identities, your goal is convert that sin(x) to the power of 4 into some sine or cosine functions to the power of 1.teng125 said:may i know how to integ (sin x^4) ??
the answer is 1/32(12x - 8sin 2x + sin4x)
So you have:teng125 said:i try to subs using cos2x=1-s(sinx)^2 but can't get
Did I tell you to use the Power-reduction formulas for cos2(2x). It's the last line of my above post (namely, the #4 post of this thread).teng125 said:ya,that's where i got stuck because i don't know how to get the sin4x.how to obtain 1/32 sin4x??
The basic concept of integrating sin x^4 is to find the antiderivative of the given function, which is the original function that when differentiated, gives the given function. In simpler terms, it is the reverse process of differentiation.
Learning how to integrate sin x^4 is important because it is a fundamental skill in calculus and is used in various fields of science and mathematics. It allows us to solve problems involving motion, optimization, and finding areas under curves.
The common techniques used for integrating sin x^4 include substitution, integration by parts, and trigonometric identities. Substitution involves replacing the variable with a new one to simplify the integral. Integration by parts is used when the integrand is a product of two functions. Trigonometric identities, on the other hand, are used to simplify the integrand.
The steps involved in integrating sin x^4 are as follows:
Some tips for integrating sin x^4 more efficiently include practicing with different types of integrals, understanding the properties of integrals, and using a table of integrals as a reference. It is also helpful to check your answer by differentiating it to ensure it is correct.