List of top Mathematics for Economy Questions on Integral Calculus

Let 𝐸 be the area of the region bounded by the curves 𝑦 = 𝑥² and 𝑦 = \(8\sqrt𝑥\), 𝑥≥0. Then 30𝐸 is equal to ________ (round off to 1 decimal place).

Let ∫ sin⁹ 𝑥 cos(11𝑥) 𝑑𝑥 = cos(10𝑥) 𝑓(𝑥) + 𝑐 , where 𝑐 is a constant. If 𝑓 ′′ (\(\frac{\pi}{4}\)) − 𝑘𝑓 ′(\(\frac{ \pi}{4}\)) = 0, then 𝑘 is equal to ______ (in integer)