Question

Интеграл от 1 до 7 (x+2) dx

Answer 1

$intlimits_1^7{(x+2)}dx=intlimits_1^7{x}dx+intlimits_1^72dx=\ =intlimits_1^7{x^1}dx+2intlimits_1^7x^0dx=\ =frac{1}{1+1}x^{1+1}|_1^7+2cdotfrac{1}{0+1}x^{0+1}|_1^7=\ =frac12x^2|_1^7+2x|_1^7=frac12(7^2-1^1)+2(7-1)=\ =frac12(49-1)+2cdot6=frac12cdot48+12=24+12=36.$