a(t)=ln(1+2^t),求该函数和t=1和t=2和x轴所成图形面积..t轴,写的时候太着急写错了...就是求积分,好久不学有点忘了
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![a(t)=ln(1+2^t),求该函数和t=1和t=2和x轴所成图形面积..t轴,写的时候太着急写错了...就是求积分,好久不学有点忘了](/uploads/image/z/14192195-59-5.jpg?t=a%28t%29%3Dln%281%2B2%5Et%29%2C%E6%B1%82%E8%AF%A5%E5%87%BD%E6%95%B0%E5%92%8Ct%3D1%E5%92%8Ct%3D2%E5%92%8Cx%E8%BD%B4%E6%89%80%E6%88%90%E5%9B%BE%E5%BD%A2%E9%9D%A2%E7%A7%AF..t%E8%BD%B4%EF%BC%8C%E5%86%99%E7%9A%84%E6%97%B6%E5%80%99%E5%A4%AA%E7%9D%80%E6%80%A5%E5%86%99%E9%94%99%E4%BA%86...%E5%B0%B1%E6%98%AF%E6%B1%82%E7%A7%AF%E5%88%86%EF%BC%8C%E5%A5%BD%E4%B9%85%E4%B8%8D%E5%AD%A6%E6%9C%89%E7%82%B9%E5%BF%98%E4%BA%86)
a(t)=ln(1+2^t),求该函数和t=1和t=2和x轴所成图形面积..t轴,写的时候太着急写错了...就是求积分,好久不学有点忘了
a(t)=ln(1+2^t),求该函数和t=1和t=2和x轴所成图形面积
..t轴,写的时候太着急写错了...就是求积分,好久不学有点忘了
a(t)=ln(1+2^t),求该函数和t=1和t=2和x轴所成图形面积..t轴,写的时候太着急写错了...就是求积分,好久不学有点忘了
x=a(t)=ln(1+2^t)
t=1 x=a(1)=ln3
t=2 x=a(2)=ln5
S=∫[1,2]ln(1+2^t)dt
1+2^t=u t=logu-1=ln(u-1)/ln2 dt=(1/ln2)du/(u-1)
=∫[3,5]lnu (1/ln2)du/(u-1)
=(1/ln2)∫[3,5]lnudu/(u-1)
∫lnudu/(u-1)=∫lnudln(u-1)
=ln(u-1)lnu-∫ln(u-1)du/u
=ln(u-1)lnu-ln(u-1)+∫du/u-∫(ln(u-1)du/u^2
=ln(u-1)lnu-ln(u-1)+lnu-ln(u-1) /u +∫du/u^2-2∫ln(u-1)du/u^3
=ln(u-1)lnu-ln(u-1)+lnu-ln(u-1)/u-1/u-2ln(u-1)/u^2+2∫du/u^3-2*3∫ln(u-1)du/u^4
=ln(u-1)lnu-ln(u-1)+lnu-ln(u-1)/u-1/u-ln(u-1)/u^2-1/u^2-2*3ln(u-1)/u^3-2/u^3-2*3*4∫ln(u-1)du/u^5
S=(1/ln2)∫[3,5]lnudu/(u-1)
=(1/ln2)[ln(u-1)lnu-ln(u-1)+lnu-ln(u-1)/u-1/u-ln(u-1)/u^2-1/u^2-2*3ln(u-1)/u^3-2/u^3 |[3,5]
-2*3*4∫[3,5]ln(u-1)du/u^5 ]
=(1/ln2)(ln5ln4-ln4+ln5-ln4/5-1/5-ln4/5^2-1/5^2-6ln4/125-2/125
-ln3ln2+ln2-ln3+ln2/3-1/3-ln2/9-1/9-6ln2/27-2/27 ]
-24∫[3,5]ln(u-1)du/u^5 ]
只能取近似值
你这几个变量了?
不知道X轴对应式中那个量?是t吗? 如果是的话,就相当于求a(t)在(1,2)上的积分。
第1题: 3种 分别是: 5元1张 2元11张 5元3张 2元6张 5元5张 2元1张 第2题:因为:3=2 2;-1 8=3 2;-1 15=4 2;-1 24=5 2;-
555