高数:积分∫[√2,0]1/(4+2x^2)dx

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高数:积分∫[√2,0]1/(4+2x^2)dx高数:积分∫[√2,0]1/(4+2x^2)dx高数:积分∫[√2,0]1/(4+2x^2)dx∫(0到√2)1/(4+2x²)dx令x=√2

高数:积分∫[√2,0]1/(4+2x^2)dx
高数:积分∫[√2,0]1/(4+2x^2)dx

高数:积分∫[√2,0]1/(4+2x^2)dx
∫(0到√2) 1/(4+2x²) dx
令x=√2*tany,dx=√2*sec²y dy
4+2x²=4+2(√2*tany)²=4+2*2*tan²y=4+4tan²y=4(1+tan²y)=4sec²y
当x=0,y=0;当x=√2,y=π/4
原式=√2*1/4∫(0到π/4) sec²y/sec²y dy
=√2/4*∫(0到π/4) dy
=√2/4*(y)(0到π/4)
=√2/4*π/4
=√2/π/16
=π/(8√2)

令x=√2tana,则dx=√2sec²ada,剩下的会算了吧

√2∏/8 (√2后面的符号是派 3。14那个