大门|大门-CS-2015（第1组）|问题54-yiteyi-C++库

$int_{frac{1}{pi}}^{frac{2}{pi}} cos(frac{1/x}{x^{2}})dx = ...........$ （A） 0 （B） -1 （C） 1. （D） 极大的 答复: （B） 说明： 设f（x）为给定函数。我们假设[frac{1}{x}=z]

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区分双方，我们得到

$[frac{-1}{x^2} dx = dz] Now, accordingly, the lower limit of the integral is [ z = frac{1}{frac{1}{pi}} = pi] and the upper limit for the integral is [ z = frac{1}{frac{2}{pi}} = frac{pi}{2}] So, the given function now becomes [ f(x)= - int_pi^{frac{pi}{2}} cos(z) dz ] [ f(x)= int_frac{pi}{2}^{pi} cos(z) dz ] [f(x) = sin(z) ,] and the upper limit is π and the lower limit is π/2 So, [f(x) = sin(pi) - sin(frac{pi}{2})] [f(x) = 0 - 1] [f(x) = -1] So, the required answer is -1.$

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