大师作文网计算定积分,要求有必要具体过程,题目内容见图.
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计算定积分,要求有必要具体过程,题目内容见图.
x = tanu,dx = sec²u du
x = 1,u = π/4
x = √3,u = π/3
[1,√3] ∫ dx / [x² √(1+x²)]
= [π/4,π/3] ∫ sec²u du / [tan²u √(1 + tan²u)]
= [π/4,π/3] ∫ cosu du / sin²u
= [π/4,π/3] ∫ dsinu / sin²u
= -1/sinu | [π/4,π/3]
=1/sin(π/4) - 1/sin(π/3)
=√2 - 2√3 /3
x = 1,u = π/4
x = √3,u = π/3
[1,√3] ∫ dx / [x² √(1+x²)]
= [π/4,π/3] ∫ sec²u du / [tan²u √(1 + tan²u)]
= [π/4,π/3] ∫ cosu du / sin²u
= [π/4,π/3] ∫ dsinu / sin²u
= -1/sinu | [π/4,π/3]
=1/sin(π/4) - 1/sin(π/3)
=√2 - 2√3 /3