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...
问题描述：
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...
答
取sinx=t
原式=∫（cost）^2/(sint)^2dt
=∫((csct)^2-1)dt
=cot-t
=pi/4-1
答
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)...