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∫(0→π/2)xsinx^2Dx

∫[0,π]x^2(sinx^2)dx =∫[0,π]x^2(1/2)(1-cos2x)dx =∫[0,π](1/2)x^2dx-∫[0,π](1/2)x^2cos2xdx =(1/6)π^3 -(1/4)∫[0,π]x^2dsin2x =(1/6)π^3+(1/2)∫[0,π]xsin2xdx =(1/6)π^3+(-1/4)∫[0,π]xdcos2x =(1/6)π^3+(-1/4)π+(1/4)∫[0,π]cos2xdx =(1/6)π^3+(...

用分步积分 S=∫(0 +∞) (sinx/x)^2 dx =x*(sinx/x)^2(0 +∞) -∫(0 +∞) xd(sinx/x)^2 =-∫(0 +∞) x*2sinx/x*(xcosx-sinx)/x^2dx =-∫(0 +∞) 2sinx/x*(xcosx-sinx)/xdx =∫(0 +∞) 2(sinx/x)^2dx-∫(0 +∞) 2sinx/x*xcosxdx =∫(0 +∞) 2(sinx/x)^2dx-...

为简化起见,以不定积分的方式,从第三个等号前开始计算。 ∫x²dsin2x =x²sin2x-∫sin2xdx² =x²sin2x-2∫xsin2xdx =x²sin2x-∫xsin2xd2x =x²sin2x+∫xdcos2x =x²sin2x+xcos2x-∫cos2xdx =x²sin2x+xcos2x-(1/2...

x(sinx)^2dx=0.5x(1-cos2x)dx=0.5xd(x-0.5sin2x) 之后再分部积分就好做了,注意三角函数的降幂

L=lim(x->0+)(sinx)^xlnL=lim(x->0+)ln(sinx)/(1/x)(∞/∞)=lim(x->0+)(cosx/sinx)/(-1/x^2)=lim(x->0+)-x^2/tanx=0L=e^0=1

利用二倍角公式,楼下用到了,但结果不对: ∫sinx^2dx =∫(1-cos2x)dx/2 =∫dx/2-(1/2)∫cos2xdx =(x/2)-(1/4)∫cos2xd(2x) =(x/2)-(1/4)sin2x+c.

∫ x sin(x²)dx = 1/2*∫ sin(x²) d(x²) = (- 1/2)cos(x²) + C 很高兴能回答您的提问,您不用添加任何财富,只要及时采纳就是对我们最好的回报 。若提问人还有任何不懂的地方可随时追问,我会尽量解答,祝您学业进步,谢谢。 ...

A 定积分(0到根号下2π)sinx^2dx > 定积分(根号下π/6到根号下π/2)sinx^2dx > 定积分(根号下π/6到根号下π/2)sin(π/6)dx > 0

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