计算：定积分∫（在上1 ,在下√2/2 ）(√1-X^2)/x^2 dx求详细过程答案,拜托大神...

令x=sint,则dx=cost dt
∫（√2/2→1）√(1-x²)/x²dx
=∫（π/4→π/2）cost/sin²t·costdt
=∫（π/4→π/2）cos²t/sin²t dt
=∫（π/4→π/2）cot²t dt
=∫（π/4→π/2）(csc²t-1) dt
=(-cot²t-t)|（π/4→π/2）
=-π/2-(-1-π/4)
=1-π/4