拜託請幫我解答
非常的急需
謝謝
1.求各曲線在區間[a,b]中繞指定的旋轉軸而成的側表面積
(1)y=x , x=€[0,1] , 旋轉軸為x軸
2.證明半徑為r的球體其表面積為4πr平方
3.∫cos(mx)dx
4.∫e^2xdx
5.∫(2x+1)(x^2+x+1)6次方dx
6.∫曲進0~1(x+1)5次方dx
7.∫ x+1
----------------------dx
x^2+2x+2
π
8.∫曲進0~ ------ sin平方x.cosdx
2
9.∫ sin√x
--------------dx
√x
可以拜託請幫我解微積分題！非常的急需~謝謝
2009-06-20 11:22 am
回答 (3)
2009-06-20 11:12 pm
✔ 最佳答案
小弟才疏學淺,只會其中幾題,請見諒!! 2.
相關證明請查閱以下網頁
http://tw.knowledge.yahoo.com/question/question?qid=1105051309532
3.
∫cos(mx)dx = (1/m)*sin(mx) + c
4.
∫e^(2x)dx = (1/2)e^(2x) + c
5.
∫(2x+1)(x^2+x+1)^6dx = (1/7)*(x^2 +x +1)^7 + c
6.
∫(x+1)^5dx [x從0~1]
=(1/6)(x+1)^6 + c │x從0~1
=(64/6) – (1/6)
=21/2
7.
∫(x+1)/(x^2 +2x +2)dx
=(1/2)*ln│x^2 +2x +2│+c
8.
∫(sin x)^2*cos xdx [x從0~π/2]
=(1/3)*(sin x)^3 + c │x從0~π/2
=1/3
9.
∫[sin(√x) / √x] dx
=-2cos(√x) +c
2009-06-21 1:53 am
你題目都是用變數變換即可
3. u = mx, du = m dx
4. u = 2x, du = 2dx
5. u = x^2 + x + 1, du = (2x + 1)dx
6. u = x + 1, du = dx
7. u = x^2 + 2x + 1, du = 2(x + 1) dx
8. u = sin x, du = cos x dx
9. u = √x, du = 1/(2√x) dx
3. u = mx, du = m dx
4. u = 2x, du = 2dx
5. u = x^2 + x + 1, du = (2x + 1)dx
6. u = x + 1, du = dx
7. u = x^2 + 2x + 1, du = 2(x + 1) dx
8. u = sin x, du = cos x dx
9. u = √x, du = 1/(2√x) dx
2009-06-21 12:27 am
收錄日期: 2021-05-04 00:45:57
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090620000010KK01422