Question

Помогите пожалуйста
∫ от 0 до 12 dx/√9*12^2-5*12x 

dee40b37f1fcda2d198156867a2ff8c5.docx

Answer 1

$intlimits^{12}_0 frac{dx}{sqrt{9cdot 12^2-5cdot 12x}}= intlimits^{12}_0 frac{dx}{sqrt{12}cdot sqrt{156-5x}} =frac{1}{sqrt{12}}cdot (-frac{1}{5})cdot 2sqrt{156-5x}left |_0^{12}=$

$=- frac{1}{5sqrt3} (sqrt{156-5cdot 12}-sqrt{156-5cdot 0})=\\=-frac{1}{5sqrt3}(sqrt{96}-sqrt{156})=-frac{1}{5sqrt3}(4sqrt6-2sqrt{39})=frac{2}{5sqrt3}(sqrt{39}-2sqrt6)$