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...

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

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...
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...

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

取sinx=t
原式=∫(cost)^2/(sint)^2dt
=∫((csct)^2-1)dt
=cot-t
=pi/4-1