Applications of integration

Use the trapezoidal rule, ∫ 𝑓(𝑥)𝑏 𝑎  𝑑𝑥 ≈ 𝑤 2 [𝑓(𝑥0)+ 2(𝑓(𝑥1)+ 𝑓(𝑥2)+ 𝑓(𝑥3)+... 𝑓(𝑥𝑛−1))+ 𝑓(𝑥𝑛)], where 𝑤 = 𝑏−𝑎 𝑛, to approximate an area and the value of a definite integral, with and without technology.