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Inequalities Between Definite Integrals

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Explanations 1

This section should be pretty intuitive: just draw a picture and the result here will be "obvious". Suppose f(x)f(x)f(x) is bounded in the interval [a,b][a,b][a,b]; that is, for…
By Calvin Lee

Problems 2

Suppose fff is continuous and bounded and has exactly three local minima in the region [a,b][a, b][a,b]: f(x1)=m1f(x_1) = m_1f(x1)=m1, f(x2)=m2f(x_2) = m_2f(x2)=m2, and f(x3…
What is the lowest integer that is an upper bound for the following integral? ∫12sin⁡(x)cos⁡(x−2) dx\int_1^2 \sin(x) \cos(x-2)\,\text{d}x∫12sin(x)cos(x−2)dx (Hint: Try graphing…