Question

高数求积分的问题

1.sin根号t/根号t dt的积分

Answer 1

1、
原式=∫-sin√t*(-1/√t)dt
=∫-sin√td√t
=cos√t+C

2、

原式=1/2∫e^(-x²)dx²
=-1/2∫e^(-x²)d(-x²)
=-1/2e^(-x²)+C

Answer 2

变量替换。
1。t=s平方
2。x平方=y

Answer 3

令根号t等于a即可。第二题将x放进去

Answer 4

因为d√t=dt/2√t
sin√tdt／√t＝2sin√td√t=-2cos√t

Answer 5

Possible intermediate steps:
integral (sin(sqrt(t)))/sqrt(t) dt
For the integrand (sin(sqrt(t)))/sqrt(t), substitute u = sqrt(t) and du = 1/(2 sqrt(t)) dt:
= 2 integral sin(u) du
The integral of sin(u) is -cos(u):
= -2 cos(u)+constant
Substitute back for u = sqrt(t):
= -2 cos(sqrt(t))+constant

简单来说，变量替换
u=根号t