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Find and prove the formula where m, n are positive integers: n ? ? if m at 11 LE cos(mx) cos(nx) dx {? ? if m = n' Hint: cos(x) cos(y) = c03(x y) + %c05(x + y) There is a line through the origin that divides the region bounded by the parabola y = x x2 and the x-axis into two regions with equal area. What is the slope of that line? Give exact answer. Hint: The two equal regions are also equal to half of the total area between the parabola and x-axis