8-5 ?稿肩???

MATLAB Τㄢよ猭ノ璸衡虫跑ㄧ计﹚縩だ

ㄒи璸衡 humps  [0, 1] ﹚縩だ

Example 1: 08-计厩ㄧ计矪瞶籔だ猂/quad01.marea = quad(@humps, 0, 1) area = 29.8583

quad の quad8 常莱ノ患癹祘狦ㄤ患癹㊣ぇΩ计笷 10 Ωㄢ贺よ猭А穦肚 Infボ┮璸衡ぇ﹚縩だぃ┪螟璸衡quad の quad8 材ま计ノㄓ﹚縩だ癸粇畉甧г

quad の quadl ノㄓ璸衡Ρ絬安砞ΤΡ絬琌パ把计てよ祘Αㄓボ

$$ \left\{ \begin{array}{l} x(t)=sin(2t)\\ y(t)=cos(t)\\ z(t)=t \end{array} \right. $$

ㄤい t 絛瞅 [0, 3$\pi$]Ρ絬瓜

Example 2: 08-计厩ㄧ计矪瞶籔だ猂/plotCurve.mt = 0:0.1:3*pi; plot3(sin(2*t), cos(t), t);

パ膀セ稬縩だΡ絬单

$$ \int_0^{3\pi} \sqrt{ \left(\frac{dx(t)}{dt}\right)^2 + \left(\frac{dy(t)}{dt}\right)^2 + \left(\frac{dz(t)}{dt}\right)^2} dt = \int_0^{3\pi} \sqrt{\left[ 4cos^2(2t)+sin^2(2t)+1 \right]} dt $$

и﹚竡ㄧ计 curveLength.m 

function out = curveLength(t) out = sqrt(4*cos(2*t).^2+sin(t).^2+1);

玥Ρ絬璸衡

Example 3: 08-计厩ㄧ计矪瞶籔だ猂/quad02.mlen = quad(@curveLength, 0, 3*pi) len = 17.2220

MATLAB  dblquad ノㄓ璸衡蛮縩だ安砞и璶璸衡

$$ \int_{x_{min}}^{x_{max}} \int_{y_{min}}^{y_{max}} f(x, y) dx dy $$

ㄤい $ f(x, y) = y sin(x) + x sin(y)$材˙艼碞琌璶ミ砆縩だㄧ计 integrand.mㄤず甧

function out = integrand(x, y) out = y*sin(x) + x*cos(y);

ゲ斗猔種琌瓃ㄧ计块ま计 xy ゲ斗㎝縩だΩdxdy璓﹚竡砆縩だㄧ计ぇи璸衡蛮縩だ

result = dblquad( 'integrand', xMin, xMax, yMin, yMax);

ㄤい

计絛ㄒ

Example 4: 08-计厩ㄧ计矪瞶籔だ猂/dblquad01.mxMin = pi; xMax = 2*pi; yMin = 0; yMax = pi; result = dblquad(@integrand, xMin, xMax, yMin, yMax) result = -9.8696

薄猵dblquad 穦㊣ quad 璸衡﹚縩だ璝斗㊣ quadl叫钡﹚ dblquad 程块把计ㄒ

Example 5: 08-计厩ㄧ计矪瞶籔だ猂/dblquad02.mxMin = pi; xMax = 2*pi; yMin = 0; yMax = pi; result = dblquad(@integrand, xMin, xMax, yMin, yMax, 'quadl') result = -9.8696

玥ヴㄏノ﹚竡縩だよ猭А砆 dblquad ㊣璶よ猭块の块ま计㎝ quad ┪ quadl 璓

Hint
  • 猔種Τ闽盽稬だよ祘Α―秆叫把ǎセ程彻盽稬だよ祘Α


MATLAB祘Α砞璸秈顶絞