What is $f (x) = \int x - sin x d x$ $f(x) = int x-sinx dx$ if $f (\frac{π}{3}) = - 6$ $f(pi/3) = -6$ ?

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What is $f (x) = \int x - sin x d x$ $f(x) = int x-sinx dx$ if $f (\frac{π}{3}) = - 6$ $f(pi/3) = -6$ ?

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Answer 1 · 2016-04-13T06:01:42

$f (x) = \frac{x^{2}}{2} + cos x - \frac{13}{2} - \frac{π^{2}}{18}$ $f(x)=x^2/2+cos x-13/2-pi^2/18$

Explanation:

Integrating, $f (x) = \frac{x^{2}}{2} + cos x + C$ $f(x)=x^2/2+cos x+C$ .
$f (\frac{π}{3}) = \frac{π^{2}}{18} + \frac{1}{2} + C = - 6$ $f(pi/3)=pi^2/18+1/2+C=-6$
$C = - \frac{13}{2} - \frac{π^{2}}{18}$ $C=-13/2-pi^2/18$

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What is $f (x) = \int x - sin x d x$ $f(x) = int x-sinx dx$ if $f (\frac{π}{3}) = - 6$ $f(pi/3) = -6$ ?

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Explanation:

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What is f(x) = int x-sinx dxf(x)=∫x−sinxdxf(x) = int x-sinx dx if f(pi/3) = -6 f(π3)=−6f(pi/3) = -6 ?

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What is $f (x) = \int x - sin x d x$ $f(x) = int x-sinx dx$ if $f (\frac{π}{3}) = - 6$ $f(pi/3) = -6$ ?