What is $f (x) = \int {sin}^{2} x - cot x d x$ $f(x) = int sin^2x-cotx dx$ if $f (\frac{5 π}{4}) = 0$ $f((5pi)/4) = 0$ ?

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What is $f (x) = \int {sin}^{2} x - cot x d x$ $f(x) = int sin^2x-cotx dx$ if $f (\frac{5 π}{4}) = 0$ $f((5pi)/4) = 0$ ?

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Answer 1 · 2017-02-22T18:42:57

$f (x) = \frac{x}{2} - \frac{sin 2 x}{4} - ln | sin x | + \frac{1}{4} - 5 \frac{π}{8} - \frac{1}{2} ln 2 .$ $f(x)=x/2-(sin2x)/4-ln|sinx|+1/4-5pi/8-1/2ln2.$

Explanation:

$f (x) = \int ({sin}^{2} x - cot x) d x .$ $f(x)=int(sin^2x-cotx)dx.$

$:. f(x)=intsin^2xdx-intcotxdx,$

$=int(1-cos2x)/2dx-ln|sinx|,$

$=1/2{int1dx-intcos2xdx}-ln|sinx|,$

$rArr f(x)=x/2-(sin2x)/4-ln|sinx|+C.$

$"To determine "C," we use the given cond. that "f(5pi/4)=0.$

$rArr 5pi/8-(sin(5pi/2))/4-ln|sin(5pi/4)|+C=0.$

$rArr 5pi/8-1/4-ln|-1/sqrt2|+C=0.$

$:. C=1/4-5pi/8-1/2ln2.$

Hence, $f(x)=x/2-(sin2x)/4-ln|sinx|+1/4-5pi/8-1/2ln2.$

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What is $f (x) = \int {sin}^{2} x - cot x d x$ $f(x) = int sin^2x-cotx dx$ if $f (\frac{5 π}{4}) = 0$ $f((5pi)/4) = 0$ ?

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Explanation:

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What is f(x) = int sin^2x-cotx dxf(x)=∫sin2x−cotxdxf(x) = int sin^2x-cotx dx if f((5pi)/4) = 0 f(5π4)=0f((5pi)/4) = 0 ?

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Explanation:

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What is $f (x) = \int {sin}^{2} x - cot x d x$ $f(x) = int sin^2x-cotx dx$ if $f (\frac{5 π}{4}) = 0$ $f((5pi)/4) = 0$ ?