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Today's calculation of Integral 138

Source: Tokyo Institute of Technology entrance exam 1968

August 12, 2006
calculusintegrationfunctiontrigonometryalgebradomainvector

Problem Statement

Let f(x)f(x) be the product of functions made by taking four functions from three functions x, sin⁡x, cos⁡xx,\ \sin x,\ \cos x repeatedly. Find the minimum value of ∫0π2f(x) dx.\int_{0}^{\frac{\pi}{2}}f(x)\ dx.
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