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vichka [17]
3 years ago
14

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

Mathematics
1 answer:
blondinia [14]3 years ago
3 0

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 = \frac{x^{n+1}}{n+1}

\int x = \frac{1}{2}x^{2}

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

Therefore:

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

Evaluate:

(\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

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