令x=(tant)^2,t∈[0,π/4]
dx=2tant(sect)^2dt
原积分=∫(0->π/4) [2tant(sect)^2 / (tant)(sect)^3]dt
=∫(0->π/4) [2cost]dt
=2sint | (0->π/4)
=√2
22题 求定积分 高数
令x=(tant)^2,t∈[0,π/4]
dx=2tant(sect)^2dt
原积分=∫(0->π/4) [2tant(sect)^2 / (tant)(sect)^3]dt
=∫(0->π/4) [2cost]dt
=2sint | (0->π/4)
=√2