∫xsin^2xdx
∫sin^2xdx=x/2-1/4sin2x+C。C为积分常数。
解答过程如下:
sin^2x=(1-cos2x)/2
∫sin^2xdx
=1/2∫1dx-1/2∫cos2xdx
=x/2-1/4∫cos2xd2x
=x/2-1/4sin2x+C
扩展资料:
二倍角公式
sin2α=2sinαcosα
tan2α=2tanα/(1-tan^2(α))
cos2α=cos^2(α)-sin^2(α)=2cos^2(α)-1=1-2sin^2(α)
常用积分公式:
1)∫0dx=c
2)∫x^udx=(x^(u+1))/(u+1)+c
3)∫1/xdx=ln|x|+c
4)∫a^xdx=(a^x)/lna+c
5)∫e^xdx=e^x+c
6)∫sinxdx=-cosx+c
7)∫cosxdx=sinx+c
8)∫1/(cosx)^2dx=tanx+c
9)∫1/(sinx)^2dx=-cotx+c
10)∫1/√(1-x^2) dx=arcsinx+c
∫xsin²x dx
=∫x*(1-cos2x)/2 dx,利用三角函数恒等式cos2x=1-2sin²x
=(1/2)∫x dx - (1/2)∫xcos2x dx
=(1/2)(x²/2) - (1/2)(1/2)∫xcos2x d(2x),凑微分
=x²/4 - (1/4)∫x d(sin2x),凑微分
=x²/4 - (1/4)[xsin2x - ∫sin2x dx],分部积分法
=x²/4 - (1/4)[xsin2x - (1/2)∫sin2x d(2x)],凑微分
=x²/4 - (1/4)[xsin2x - (1/2)(-cos2x)] + C
=x²/4 - (1/4)xsin2x - (1/8)cos2x + C,注意头一项的是x²而不是x
=1/2∫x(1-cos2x)dx
=1/4x^2-1/2∫xcos2xdx
=1/4x^2-1/4∫xdsin2x
=1/4x^2-1/4xsin2x+1/4∫sin2xdx
=1/4x^2-1/4xsin2x-1/8cos2x+C
微积分 微分计算 ∫xsin^2xdx=?
∫xsin^2xdx =1\/2∫x(1-cos2x)dx =1\/4x^2-1\/2∫xcos2xdx =1\/4x^2-1\/4∫xdsin2x =1\/4x^2-1\/4xsin2x+1\/4∫sin2xdx =1\/4x^2-1\/4xsin2x-1\/8cos2x+C
计算不定积分∫xsin^2xdx
先降幂,再求积分 答案如图所示
∫xsin^2xdx
∫xsin^2xdx =1\/2∫x(1-cos2x)dx =1\/4x^2-1\/2∫xcos2xdx =1\/4x^2-1\/4∫xdsin2x =1\/4x^2-1\/4xsin2x+1\/4∫sin2xdx =1\/4x^2-1\/4xsin2x-1\/8cos2x+C
∫xsinxsinxdx的不定积分
用分部积分法 ∫xsin^2xdx=0.5∫x(1-cos2x)dx =0.5∫xdx-0.25∫xdsin2x =0.25x^2-0.25xsin2x+0.25∫sin2xdx =0.25x^2-0.25xsin2x-0.125cos2x+C
定积分∫上π下-π xsin^2xdx 等于多少
"原式=1\/2*(∫[x(1-cos2x)]dx)=1\/2[∫xdx-1\/2*∫xdsin2x]=1\/2[(π--π)-1\/2*(xsin2x-∫sin2xdx)]=1\/2*[2π-1\/2*(0+cos2x\/2)]=π"
∫0到π xsin^2xdx?
xdx =∫(0,π)(π-x)sin²(π-x)dx =∫(0,π)(π-x)sin²(x)dx =∫(0,π)[πsin²(x)dx-∫(0,π)xsin²xdx ∴2∫(0,π)xsin²xdx=∫(0,π)πsin²(x)dx ∫(0,π)xsin²xdx=½π∫(0,π)sin²(x)dx ...
∫e^xsin^2xdx
先降幂,再求积分就行,答案如图所示
不定积分过程、、、
∫e^xsin^2xdx = ∫e^x(1-cos(2x))\/2dx = 1\/2 e^x - 1\/2 ∫e^x cos(2x)dx 而 ∫e^x cos(2x)dx = 1\/2 ∫e^x d[sin(2x)]= 1\/2 [ e^x [sin(2x)] - ∫e^x [sin(2x)] dx ]= 1\/2 [ e^x [sin(2x)] + 1\/2 [ ∫e^x d[cos(2x)] ]= ...
∫x^3 sin^2xdx
x^3sin^2x dx = ∫ x^3 (1 - cos(2x))\/2 dx = (1\/8)x^4 - (1\/2)K where K = ∫ x^3cos(2x)dx 令f = x^3 and g = cos(2x),以下分别对f求导,对g求积分 f = x^3 g = cos2x f'= 3x^2 g(1)= (1\/2)sin(2x)f''= 6x g(2)= (- 1\/4)cos(2x)f'...
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