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...

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)...