Solving the Integral: $\int \sin^2 x \cos x \,dx$

tandoorichicken · 2003-12-18T05:45:45+00:00

need help with this: \int \sin^2 x \cos x \,dx

Thread starter tandoorichicken
Start date Dec 17, 2003
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Integral

In summary, the first step in solving this integral is to use the trigonometric identity sin^2 x = (1-cos2x)/2. This integral can be solved using the substitution method by letting u = cosx and du = -sinx dx. The general formula for solving integrals of the form ∫ sin^m x cos^n x dx is to use the trigonometric identity sin^2 x = (1-cos2x)/2 and then apply the power reduction formula cos^n x = (1+cos2x)^n/2^n. The final answer to this integral is (-1/4)cos^3 x + C, where C is the constant of integration. Besides the substitution

Dec 17, 2003

tandoorichicken

need help with this:

[tex] \int \sin^2 x \cos x \,dx [/tex]

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Dec 17, 2003

tandoorichicken

nevermind, tactical error :)

Dec 18, 2003

himanshu121

With these kind of problems show ur attempt before

FAQ: Solving the Integral: $\int \sin^2 x \cos x \,dx$

What is the first step in solving this integral?

The first step in solving this integral is to use the trigonometric identity sin^2 x = (1-cos2x)/2.

Can this integral be solved using substitution?

Yes, this integral can be solved using the substitution method. Let u = cosx, then du = -sinx dx.

What is the general formula for solving this type of integral?

The general formula for solving integrals of the form ∫ sin^m x cos^n x dx is to use the trigonometric identity sin^2 x = (1-cos2x)/2 and then apply the power reduction formula cos^n x = (1+cos2x)^n/2^n.

What is the final answer to this integral?

The final answer to this integral is (-1/4)cos^3 x + C, where C is the constant of integration.

Are there any other methods for solving this integral?

Yes, besides the substitution method, this integral can also be solved using integration by parts or by converting it to a simpler form using trigonometric identities.