1) a) Int (1; 2) x dx = x^2/2 | (1; 2) = 2^2/2 - 1^2/2 = 2 - 1/2 = 3/2
b) Int (pi/2; pi) sin x dx = -cos x | (pi/2; pi) = -cos pi - (-cos pi/2) = -(-1) - 0 = 1
c) Int (pi/6; pi/4) dx / cos^2 x = tg x | (pi/6; pi/4) = tg pi/4 - tg pi/6 = 1 - √3/3
2) a) Int (0; 3) x^2 dx = x^3/3 | (0; 3) = 3^3/3 - 0 = 27/3 = 9
b) Int (0; pi) sin x dx = -cos x | (0; pi) = -cos pi - (-cos 0) = -(-1) - (-1) = 2
c) Int (1/4; 1) dx/x = ln x |(1/4; 1) = ln 1 - ln (1/4) = 0 - (-ln 4) = ln 4