Question

In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?

Options

• \[\int(1-\sin^2x)\sin^2x(\cos x)\,dx\]

• \[\int\sin^2x\cos^2x(\sin x)\,dx\]

• \[\int\sin^2x\cos x(\sin x)\,dx\]

• \[\int\sin^3x\cos x(\cos x)\,dx\]

Answer 1

One factor \[\sin x\] is separated because \[dt=-\sin x\,dx\]. The remaining \[\sin^2x\] can then be written using \[1-\cos^2x\].