cos25πtdt (0~π/4)的微积分怎么求?f(0~π/4)cos25πtdt麻烦过程详细一点,这里的dt什么意思?原函数是(sin25πt)/25π吗?谢谢~!

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cos25πtdt (0~π/4)的微积分怎么求?
f(0~π/4)cos25πtdt
麻烦过程详细一点,这里的dt什么意思?原函数是(sin25πt)/25π吗?
谢谢~!

∫(0~π/4)cos25πtdt
=1/(25π)∫(0~π/4)cos25πtd25πt
=1/(25π)sin25πt (0~π/4)
=1/(25π)[sin(25π*π/4)-sin0]
=sin(25π²/4)/(25π)

答:
(0→π/4) ∫ cos(25πt) dt
=(0→π/4) (1/25π)* ∫cos(25πt) d(25πt)
=(0→π/4) sin(25πt) /(25π)
=sin(25π²/4) /(25π)
dt是微元、微分,cos(25πt)的原函数是sin(25πt)/(25π)