What is $f (x) = \int x - sin 2 x - 6 cos x d x$ $f(x) = int x-sin2x-6cosx dx$ if $f (\frac{π}{2}) = 3$ $f(pi/2)=3$ ?

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What is $f (x) = \int x - sin 2 x - 6 cos x d x$ $f(x) = int x-sin2x-6cosx dx$ if $f (\frac{π}{2}) = 3$ $f(pi/2)=3$ ?

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Answer 1 · 2016-12-22T12:40:29

$f (x) = \frac{x^{2}}{2} + \frac{1}{2} cos 2 x - 6 sin x + \frac{7}{2} - \frac{π^{2}}{8}$ $f(x)=x^2/2+1/2cos2x-6sinx+7/2-pi^2/8$

Explanation:

$f (x) = \int (x - sin 2 x - 6 cos x) d x$ $f(x)=int(x-sin2x-6cosx)dx$ $f (\frac{π}{2}) = 3$ $" "f(pi/2)=3$

integrate term by term

$f (x) = \frac{x^{2}}{2} + \frac{1}{2} cos 2 x - 6 sin x + C$ $f(x)=x^2/2+1/2cos2x-6sinx+C$

$f (\frac{π}{2}) = \frac{1}{2} \times {(\frac{π}{2})}^{2} + \frac{1}{2} cos (2 \times \frac{π}{2}) - 6 sin (2 \times \frac{π}{2}) + C = 3$ $f(pi/2)=1/2xx(pi/2)^2+1/2cos(2xxpi/2)-6sin(2xxpi/2)+C=3$

$pi^2/8+1/2cancel(cospi)^-1- 6cancel(sinpi)^0+C=3$

$pi^2/8-1/2+C=3$

$C=3+1/2-pi^2/8=7/2-pi^2/8$

$f(x)=x^2/2+1/2cos2x-6sinx+7/2-pi^2/8$

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What is $f (x) = \int x - sin 2 x - 6 cos x d x$ $f(x) = int x-sin2x-6cosx dx$ if $f (\frac{π}{2}) = 3$ $f(pi/2)=3$ ?

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What is f(x) = int x-sin2x-6cosx dxf(x)=∫x−sin2x−6cosxdxf(x) = int x-sin2x-6cosx dx if f(pi/2)=3 f(π2)=3f(pi/2)=3 ?

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What is $f (x) = \int x - sin 2 x - 6 cos x d x$ $f(x) = int x-sin2x-6cosx dx$ if $f (\frac{π}{2}) = 3$ $f(pi/2)=3$ ?