∫（√2/2，1）【√（1-x^2）】/x^2dx
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令x=sin t，则dx=cost dt
当x=√2/2时，t=π/4；当x=1时，t=π/2.
故原式=∫[π/4，π/2] cost /sin²t · costdt
=∫[π/4，π/2]cos²t /sin²t dt
=∫[π/4，π/2](1/sin²t -1)dt
=(-cot t -t)|[π/4，π/2]
=(0-π/2)-(-1 -π/4)
=1 - π/4
当x=√2/2时，t=π/4；当x=1时，t=π/2.
故原式=∫[π/4，π/2] cost /sin²t · costdt
=∫[π/4，π/2]cos²t /sin²t dt
=∫[π/4，π/2](1/sin²t -1)dt
=(-cot t -t)|[π/4，π/2]
=(0-π/2)-(-1 -π/4)
=1 - π/4
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