Question

Интеграл от 1 до 7 (x+2) dx

Answer 1

$\int\limits_1^7{(x+2)}dx=\int\limits_1^7{x}dx+\int\limits_1^72dx=\\ =\int\limits_1^7{x^1}dx+2\int\limits_1^7x^0dx=\\ =\frac{1}{1+1}x^{1+1}|_1^7+2\cdot\frac{1}{0+1}x^{0+1}|_1^7=\\ =\frac12x^2|_1^7+2x|_1^7=\frac12(7^2-1^1)+2(7-1)=\\ =\frac12(49-1)+2\cdot6=\frac12\cdot48+12=24+12=36.$