Toán 12.Tích phân hàm lượng giác.

V

vht2007

[TEX]\int\limits_{\pi/3}^{\pi/2}\frac{\sqrt[3]{sin^3 x - sin x} cot x}{sin^3 x} dx=\int\limits_{\pi/3}^{\pi/2}\frac{\sqrt[3]{sin^3 x - sin x} cos x }{sin^4 x} dx[/TEX]

Đặt [tex] t = sin x => dt = cosx.dx [/tex]

[tex] => I = \int\limits_{\frac{\sqrt3}{2}}^{1}\frac{\sqrt[3]{t^3 - t }}{t^4} dt [/tex]
 
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N

nghianghialan

vht2007 said:
[TEX]\int\limits_{\pi/3}^{\pi/2}\frac{\sqrt[3]{sin^3 x - sin x} cot x}{sin^3 x} dx=\int\limits_{\pi/3}^{\pi/2}\frac{\sqrt[3]{sin^3 x - sin x} cos x }{sin^4 x} dx[/TEX]

Đặt [tex] t = sin x => dt = cosx.dx [/tex]

[tex] => I = \int\limits_{\frac{\sqrt3}{2}}^{1}\frac{\sqrt[3]{t^3 - t }}{t^4} dt [/tex]
Bấm để xem đầy đủ nội dung ...
[TEX]\int_{}^{}\frac{\sum_{k=0}^{\frac{1}{3}}(-1) C_{\frac{1}{3}}^kt^3{(\frac{1}{3}-k)}.t^k}{t^4}[/TEX]
[TEX]\int_{}^{}\sum_{k=0}^{\frac{1}{3}}(-1) C_{\frac{1}{3}}^kt^{14}}[/TEX]
[TEX]\frac{\sum_{k=0}^{\frac{1}{3}}(-1) C_{\frac{1}{3}}^k t^{15}}{{15}[/TEX]
thay can vao af ok thoi
 
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L

letuananh1991

bài này giải ......

[TEX]\int_{\frac{\pi}{2}}^{\frac{\pi}{3}} \frac{1}{(sinx)^2}cotx\sqrt[3]{1-\frac{1}{(sinx)^2}} dx[/TEX]

[TEX]= \int_{\frac{\pi}{2}}^{\frac{\pi}{3}}cotx\sqrt[3]{-(cotx)^2} d(cotx)[/TEX]

đến đây thì ok rồi.........
 
V

vodichhocmai

henry14 said:
Tính tích phân:


[TEX]\int\limits_{\pi/3}^{\pi/2}\sqrt[3]{sin^3 x - sin x} cot x/sin^3 x[/TEX]
Bấm để xem đầy đủ nội dung ...


[TEX]\int_{\frac{\pi }{3}}^{\frac{\pi }{2}}\frac{\sqrt[3]{1-\frac{1}{sin^2x}}}{sin^2x}.cotxdx[/TEX]

[TEX]\ \ \ \ t=cotx\righ dt=-\frac{1}{sin^2x}dx[/TEX]

[TEX]I=\int_{0}^{\frac{1}{\sqrt{3}}}-t.\sqrt[3]{t^2}dt[/TEX]

[TEX]\ \ \ \ u=\sqrt[3]{t^2}\righ 3u^2=2tdt[/TEX]

[TEX]I=-\frac{3}{2}\int_{0}^{\frac{1}{\sqrt[3]{3}}}u^3du=OK[/TEX]
 
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