Bantuin yaintegral sin^2 x / 1-cos x dx = ?note ^=pangkat.... Question from @rahmanggraeni8

August 2018 2 60 Report

Bantuin ya
integral sin^2 x / 1-cos x dx = ?
note ^=pangkat

acim $\int\ \frac{sin^{2}x}{1-cosx}dx \\\\ = \int\ \frac{sin^{2}x}{1-cosx} . \frac{1+cosx}{1+cosx} dx \\ \\ = \int\ \frac{sin^{2}x(1+cosx)}{1- cos^{2}x}dx \\ \\ = \int\ \frac{sin^{2}x(1+cosx)}{ sin^{2}x }dx \\ \\ = \int\ (1+cosx) dx \\ \\ = x + sinx + C$

1 votes Thanks 1

jenersonotniel $\int\limits \frac{sin^{2}x}{1-cosx} \, dx= \int\limits \frac{sin^{2}x}{1-cosx}. \frac{1+cosx}{1+cosx} \, dx= \int\limits \frac{(sin^{2}x)(1+cosx)}{(1-cosx)(1+cosx)} \, dx$ $=\int\limits \frac{(sin^{2}x+sin^{2}cosx)}{1-cos^{2}x} \,=\int\limits \frac{(sin^{2}x+sin^{2}cosx)}{sin^{2}x} =\int\limits \frac{sin^{2}x(1+cosx)}{sin^{2}x} \,$ $=\int\limits (1+cosx)=x+(-sinx)+C=x-sinx+C$

:)

1 votes Thanks 1

acim basic : integral of cos(x) dx = sin(x) integral of sin(x) dx = - cos(x) derivative of sin(x) = cos(x) derivative of cos(x) = -sin(x) They are must be in your book, :P

Bantu lagi yaa pleaseintegral (4+ 2 tankuadrat x) dx = ?

Please bantu yaberapakah integral sin kuadrat x / 1-cos x dx ?

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