khoa thay le ba tran phuong

H

hhhaivan

Ý bạn là :

[TEX] I= \int_{0}^{\frac{\pi}{2}} \frac{4sin^3x}{2+cosx}dx[/TEX]

[TEX]\Leftrightarrow I=\int_{0}^{\frac{\pi}{2}} \frac{4sin^2xsinx}{2+cosx}dx[/TEX]

[TEX]\Leftrightarrow I=\int_{0}^{\frac{\pi}{2}} \frac{4(1-cos^2x)sinx}{2+cosx}dx[/TEX]

[TEX] {Dat}\ t = 2 + cosx \Rightarrow dt= - sinxdx \Rightarrow sinxdx = -dt[/TEX]

[TEX] I= 4 \int_{2}^{3} \frac{1-(t-2)^2}{t}dt[/TEX]

[TEX]\Leftrightarrow I= 4 \int_{2}^{3} ( -t + 4 + \frac{-3}{t})dt[/TEX]

[TEX]\Leftrightarrow I = 4 [ -(\frac{t^2}{2})\mid_{2}^{3}+ 4(t)\mid_{2}^{3} - 3(|lnt|)\mid_{2}^{3} ][/TEX]
 
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