Криволинейни интеграли във векторни полета

Дадено е векторното поле $f(x; y) = (x; \cos(y))$f, left parenthesis, x, ;, y, right parenthesis, equals, left parenthesis, x, ;, cosine, left parenthesis, y, right parenthesis, right parenthesis и крива $C$C с параметризация $\alpha(t) = \left( t^2, t \right)$alpha, left parenthesis, t, right parenthesis, equals, left parenthesis, t, squared, comma, t, right parenthesis в интервала $0 < t < 2$0, is less than, t, is less than, 2.

$\displaystyle \int_C f \cdot d\alpha =$integral, start subscript, C, end subscript, f, dot, d, alpha, equals