Question

Помогите с решением интегралов

Answer 1

$\displaystyle \int (cos^42x-sin^22x)dx=\int (cos^22x-sin^22x)(cos^22x+sin^22x)dx=\\\\=\int cos4x*dx=\bigg|4x=t;4dx=dt\bigg|=\int cost*\frac{dt}{4}=\frac{1}{4}sint+C=\frac{sin4x}{4}+C$

$\displaystyle \int\limits^\pi _{-2\pi } {sinx}*dx=-cosx\bigg|^{\pi }_{-2\pi }=-(cos\pi -cos(-2\pi ))=-(-1-1)=2$