求定积分∫XedX上|下o上X
来源:学生作业帮助网 编辑:作业帮 时间:2024/05/15 18:32:40
再问:x-1=sint,是设的?再答:是的再问:0和-π/2是咋取得,是sin还是cos再答:换元换限
见图,此积分的几何意义是1-x在[0,1]内的部分与x轴所围的图形的面积.令1-x与x和y轴的交点分别为A(1,0),B(0,1)S=(1/2)*OA*OB=(1/2)*1*1 =1/2
∫[0,1]1/(x^2-2x-3)dx=1/5∫[0,1][1/(x-3)-1/(x+2)]dx=1/5[ln|x-3|-ln|x+2|][0,1]=1/5(ln2-ln3-ln2+ln2)=0
令√(1+x)=t,则x=t^2-1原式=∫(1→2)(t^2-1)/(t+1)*2tdt=∫(1→2)2t(t+1)dt=∫(1→2)2t^2dt+∫(1→2)2tdt=2/3t^3|(1→2)+t
要找到x-1的原函数.x的原函数为x²/2,也就是x²/2的导数为x.-1的原函数为-x.所以x-1的原函数为(x²/2)-x所以积分值为:3²/2-3=9/2
∫[1,0]dx/(x²-2x-3)=∫[1,0]dx/[(x-3)(x+1)]=(1/4)∫[1,0][1/(x-3)-1/(x+1)]dx=(1/4)ln|(x-3)/(x+1)|=(1
-(1-exp(-6243314768165359/4503599627370496))^(1/2)-1/2*log(1-(1-exp(-6243314768165359/45035996273704
∫上1下0e^x(1+e^x)^3dx=∫上1下0(1+e^x)^3d(e^x)=∫上1下0(1+e^x)^3d(1+e^x)=(1/4)(1+e^x)^4|=(1/4)[(1+e^1)^4-(1+e
∫上2下1[(x/2)-(1/x)-(1/x^2)]dx=∫上2下1[(x/2)-x^(-1)-x^(-2)]dx=[(1/4)x^2-lnx+(1/x)]|=[(1/4)2^2-ln2+1/2]-[
1/[x根号(x²-1)]设x=sectx=(根号2)时,t=π/4x=2时,t=π/6原式化为::dx=dsect=tant*sectdt∫(π/6,π/4)tantsectdt/(sec
由题意可得:先求∫√(x^2-1)/xdx的不定积分令√(x^2-1)=t,又上下限均大于0所以x=√(t^2+1),dx=t/√(t^2+1)dt所以∫√(x^2-1)/xdx=∫t/√(t^2+1
∫0~√(ln2)x×e^(x^2)dx=1/2×∫0~√(ln2)2x×e^(x^2)dx=1/2×∫0~√(ln2)e^(x^2)d(x^2)令t=x^2=1/2×∫0~(ln2)e^tdt=1/
y=√[9-(x-3)²](x-3)²+y²=3²圆心(3,0),半径3由0到6,正好围绕一个半圆所以∫(0→6)√[9-(x-3)²]dx=1/2·
∫(2~3)(1-x)/x²dx=∫(2~3)(1/x²-1/x)dx=-1/x-lnx|(2~3)=(-1/3-ln3)-(-1/2-ln2)=ln(2/3)+1/6
∫上e下1lnxdx=x*lnx上e下1-∫上e下1dx=e-(e-1)=1
∫[0,√2](x/4+x^4)dx=1/2∫[0,√2](1/4+x^4)dx^2=1/2*1/2arctan(x^2/2)[0,√2]=π/16再问:∫上根号2下0再答:对啊
=*d(1+e^x)=1/4*(1+e^x)^4