>> x=-4:0.1:4;
>> y=x.^(2/3).*(x.^2-8); >> plot(x,y)
从图看出函数有极大极小值。 >> f='x.^(2/3).*(x.^2-8)'; >> xmin=fminbnd(f,-4,4)
xmin =
1.278404849559600 - 0.260098701930077i
>> x=xmin;
>> miny=x.^(2/3).*(x.^2-8)
miny =
-7.718305008002356 + 0.237838653225849i
>> x=-4:0.1:4;
>> f='-x.^(2/3).*(x.^2-8)'; >> xmax=fminbnd(f,-4,4)
Exiting: Maximum number of function evaluations has been exceeded - increase MaxFunEvals option. Current function value: -3.905290
xmax =
-1.506656018341058 + 0.169172989824599i
>> x=xmax;
>> maxy=x.^(2/3).*(x.^2-8) maxy =
3.905290280403644 - 6.554360315624097i
(3)f(x)?x3?4x2?3x >> x=-2:0.1:4;
>> y=x.^3-4.*x.^2-3.*x; >> plot(x,y)
从图看出函数有极大极小值。 >> f='x.^3-4.*x.^2-3.*x'; >> xmin=fminbnd(f,-4,4)
xmin =
2.999998479983027
>> x=xmin;
>> miny=x.^3-4.*x.^2-3.*x miny =
-17.999999999988447
>> x=-2:0.1:4;
>> f='-(x.^3-4.*x.^2-3.*x)'; >> xmax=fminbnd(f,-4,4)
xmax =
-0.333331121184471
>> x=xmax;
>> maxy=x.^3-4.*x.^2-3.*x maxy =
0.518518518494050
(5)f(x)?>> syms x y=(log(x)).^2/x; y1=diff(y) y1 =
2*log(x)/x^2-log(x)^2/x^2
>> x0=solve(y1)
xmin=fminbnd('(log(x)).^2/x',0.5, 9) x=xmin; miny=(log(x)).^2/x x0 = 1 exp(2)
1xln2x
xmin =
1.000000702315345
miny =
4.932461516052710e-013
>> xmax=fminbnd('-((log(x)).^2/x)',0.5, 9) xmax =
7.389063295324329
Q14:求下列不定积分：
(1)?sinxcosx1?sin4xdx
>> syms x
>> f=sin(x)*cos(x)/(1+sin(x)*4); >> int(f,x)
ans =
1/4*sin(x)-1/16*log(1+4*sin(x)) (3)?arcsinx1?xdx
>> syms x
>> f=asin(x)/sqrt(1-x); >> int(f,x) ans =
-2*(1-x)^(1/2)*asin(x)-4*(1-x)^(1/2)*(-1-x)/(2-2*x-(1-x)^2)^(1/2) (5)?x?x?4x?2x(x?1)322642dx
>> syms x
>> f=(x^6+x^4-4*x^2-2)/(x^3*((x^2+1)^2)); >> int(f,x)
ans =
1/2*log(x^2+1)+1/x^2-1/(x^2+1)
Q15:求下列定积分：
(2)?x2(2?3x2)2dx
01>> syms x
>> int('x^2*(2-3*x^2)',0,1) ans = 1/15
?(4)?2sin5xcos4xdx
0>> syms x
>> int('sin(5*x)*cos(4*x)',0,pi/2) ans = 5/9 (6)?2?0xcosxdx
2>> syms x
>> int('x*(cos(x)^2)',0,pi*2) ans = pi^2
Q17:用三种方法求下列积分的数值解：
(1)?e?0.5xsin?x?03?????dx 6?精确值为： >> syms x
>> int('exp(-0.5*x)*sin(x+pi/6)',0,3) ans =