∫上2下1fxdx怎么算

任点施2904微积分求解:∫上2下1(2/x)dx请写出解答过程,我想知道既然(x^n)'=nx^(n - 1)要求n不为0,那这道题要如何解答? -
尚采广17271107734 ______[答案] ∫上2下1(2/x)dx =2lnx |上2下1=2ln2-2ln1=2ln2

任点施2904求定积分∫上2下1 [(x/2) - (1/x) - (1/x^2)]dx -
尚采广17271107734 ______[答案] ∫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]-[(1/4)1^2-ln1+1] =1/4-ln2

任点施2904求不定积分或定积分∫(上2 下 - 1) |x|dx -
尚采广17271107734 ______ 解:∫|x|dx=∫<0,2>xdx+∫(-x)dx =(2^2-0^2)/2-(0^2-(-1)^2)/2 =2+1/2 =5/2.

任点施2904积分号上面是2下面0x(1 - x)dx,这个具体步骤怎莫算? -
尚采广17271107734 ______ ∫[0,2]x(1-x)dx =∫[0,2](x-x²)dx =x²/2-x³/3+C [0,2] =2-8/3-0 =-2/3

任点施2904求∫上限为2下限为1(x - 1)dx的近似值 -
尚采广17271107734 ______ 原式=(1/2x^2-x)|(1→2)=1/2 我不理解“近似值”是怎么回事……

任点施2904∫(上x下1)f(x)dx=1/2(x)^4则∫(上4下1)f(根号x)/根号(x)dx -
尚采广17271107734 ______[答案] ∫(上x下1)f(x)dx=1/2(x)^4 求导得到 f(x)=2x^3, 那么f(根号x)=2x *根号x 所以 ∫(上4下1)f(根号x)/根号(x)dx =∫(上4下1) 2xdx =x^2 (代入上下限4和1) =16-1 =15

任点施2904计算∫上限2下限1 1/(1+根号下2X) dx -
尚采广17271107734 ______[答案] 2-√2-ln3+ln(1+√2)

任点施2904求定积分∫上1下0 e^x(1+e^x)^3dx -
尚采广17271107734 ______[答案] ∫上1下0 e^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^0)^4] =(1/4)[(1+e)^4-2^4] =[(1+e)^4-16]/4

任点施2904计算∫上1下0,x根号下x+1dx -
尚采广17271107734 ______[答案] =∫x(根号下x+1)dx =∫(x+1)(根号下x+1)d(x +1)-∫(根号下x+1)d(x +1)=2/5*(x +1)^(5/2)-2/3*(x +1)^(3/2)=4(√2+1)/15

任点施2904∫下1上e X^2Inxdx -
尚采广17271107734 ______[答案] ∫下1上e X^2Inxdx = ∫下1上e Inxd(x³/3) =x³/3lnx|(1,e)-∫(1,e)x²/3dx =e³/3-x³/9|(1,e) =e³/3-e³/9+1/9 =2e³/9+1/9