quizz matematika


Forum matematika
\int sin^5(x)dx
sin^5(x)=sin^4(x).sin(x)=\int sin^4(x).sin(x)dx
sin^4(x)=(sin^4(x))^2=\int (sin^2(x))^2.sin(x)dx
sin^2(x)=1-cos^2(x)=\int (1-cos^2(x))^2.sin(x)dx
subtitusikan dgn rumus
\int f(g(x)).g(x)dx=\int f(u)du;u=g(x),u=cos(x),du=-sin(x)dx
=\int -(1-u^2)^2du\rightarrow \int a.f(x)dx=a\int f(x)dx
=\int (-u^2)^2du
=-\int (u^2-1)^2du
=-\int (u^4-2u^2+1)du
Gunakan rumus integral
\int f(x)=\pm g(x)dx-\int f(x)dx\pm\int g(x)dx
=-\int u^du-\int 2u^2du+\int 1du
=\int u^4du=\frac{u^5}{5}
\int 2u^2du=\frac{2u^3}{3}
=\int 1du=u
=-(\frac{u^5}{5}-\frac{2u^3}{3}+u)
subtitusikan kembali
u=cos(x)
-(\frac{cos^5(x)}{5}-\int \frac{2cos^3(x))}{3}+cos(x))
=-\frac{1}{5}cos^5(x)+\frac{2cos^3(x)}{3}-cos(x)+C

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