Hi there!
[tex]\boxed{= 70 + cos(12) - cos(2) \approx 71.26}[/tex]
[tex]\int\limits^{12}_{2} {x-sin(x)} \, dx[/tex]
We can evaluate using the power rule and trig rules:
[tex]\int x^n = \frac{x^{n+1}}{n+1}[/tex]
[tex]\int x = \frac{1}{2}x^{2}[/tex]
[tex]\int -sin(x) = cos(x)[/tex]
Therefore:
[tex]\int\limits^{12}_{2} {x-sin(x)} \, dx = [\frac{1}{2}x^{2}+cos(x)]_{2}^{12}[/tex]
Evaluate:
[tex](\frac{1}{2}(12^{2})+cos(12)) - (\frac{1}{2}(2^2)+cos(2))\\= (72 + cos(12)) - (2 + cos(2))\\\\= 70 + cos(12) - cos(2) \approx 71.26[/tex]
