Question

含有参数的定积分题目怎么求

Answer 1

一般这都通过分部积分把它变为递推公式，然后归纳出通项公式
题目1令x=sint带入后，可以变为(cost)^(m+1)
dt的积分
它和题目2计算类似
以2为例子(S表示积分）
Jm
=
-S[x(sinx)^(m-1)dcosx]
=
xcosx(sinx)^(m-1)
-
(m-1)S[x(sinx)^(m-2)(cosx)^2dx]
=
xcosx(sinx)^(m-1)
-
(m-1)S[x(sinx)^(m-2)[1-(sinx)^2dx]]
=xcosx(sinx)^(m-1)
-
(m-1)J(m-2)
+(m-1)Jm
这样就由个递推公式了，利用数列知识归纳出公式即可

Answer 2

warning:
warning,
unable
to
determine
if
r+1/2*m
is
between
0
and
m;
try
to
use
assumptions
or
set
_envallsolutions
to
true
warning:
warning,
unable
to
determine
if
-r+1/2*m
is
between
0
and
m;
try
to
use
assumptions
or
set
_envallsolutions
to
true
warning:
warning,
unable
to
determine
if
1/2*m-1/2*(-t*(t+4*r))^(1/2)
is
between
0
and
m;
try
to
use
assumptions
or
set
_envallsolutions
to
true
warning:
warning,
unable
to
determine
if
1/2*m+1/2*(-t*(t+4*r))^(1/2)
is
between
0
and
m;
try
to
use
assumptions
or
set
_envallsolutions
to
true
warning:
explicit
integral
could
not
be
found.
>
in
sym.int
at
58
in
untitled
at
6
int_y
=
int(1/(t+2*r-(4*r^2-m^2+4*m*x-4*x^2)^(1/2)),x
=
0
..
m)
你的这个
表达式
太复杂了。matlab用现有
的方法
求不出来