Integral dari sin 11x sin 5x

Integral dari sin 11x sin 5x

Jawab:

$displaystyle intsin11xsin5x,dx=intfrac{cos(11x-5x)-cos(11x+5x)}{2},dx\intsin11xsin5x,dx=frac12int(cos6x-cos16x),dx\intsin11xsin5x,dx=frac12left(frac16sin6x-frac1{16}sin16xright)+C\intsin11xsin5x,dx=frac1{12}sin6x-frac1{32}sin16x+C$

Beberapa konsep yang dipakai:

$displaystyle triangleright~sin asin b=frac{cos(a-b)-cos(a+b)}{2}\triangleright~int ky,dx=kint y,dx\triangleright~int y_1pm y_2pmcdotspm y_n,dx=int y_1,dxpmint y_2,dxpmcdotspmint y_n,dx\triangleright~intcos ax,dx=frac1asin ax+C$