Question

The value of the definite integral / 212x – sin(x) dx / 122x-sin(x) is

Answer 1

Hi there!

`\boxed{= 70 + cos(12) - cos(2) \approx 71.26}`

`\int\limits^(12)_(2) {x-sin(x)} \, dx`

We can evaluate using the power rule and trig rules:

`\int x^n = (x^(n+1))/(n+1)`

`\int x = (1)/(2)x^(2)`

`\int -sin(x) = cos(x)`

Therefore:

`\int\limits^(12)_(2) {x-sin(x)} \, dx = [(1)/(2)x^(2)+cos(x)]_(2)^(12)`

Evaluate:

`((1)/(2)(12^(2))+cos(12)) - ((1)/(2)(2^2)+cos(2))\\= (72 + cos(12)) - (2 + cos(2))\\\\= 70 + cos(12) - cos(2) \approx 71.26`