What is $f (x) = \int x - x^{2} sec x d x$ $f(x) = int x-x^2secx dx$ if $f (\frac{π}{4}) = 3$ $f(pi/4)=3$ ?

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What is $f (x) = \int x - x^{2} sec x d x$ $f(x) = int x-x^2secx dx$ if $f (\frac{π}{4}) = 3$ $f(pi/4)=3$ ?

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Answer 1 · 2018-08-13T21:07:08

$\int (x - x^{2}) d x = \frac{x^{2}}{2} - \frac{x^{3}}{3} + 3 + \frac{π^{3}}{192} - \frac{π^{2}}{32}$ $int(x-x^2)dx=x^2/2-x^3/3+3+pi^3/192-pi^2/32$ if $f (\frac{π}{4}) = 3$ $f(pi/4)=3$

Explanation:

$I = \int (x - x^{2}) d x$ $I=int(x-x^2)dx$

$= \int x d x - \int x^{2} d x$ $=intxdx-intx^2dx$

$= \frac{x^{2}}{2} - \frac{x^{3}}{3} + C$ $=x^2/2-x^3/3+C$ , $C in RR$

Also, $f(pi/4)=3$

$(pi/4)^2/2-(pi/4)^3/3+C=3$

$C=3+pi^3/192-pi^2/32$

Finally, $I=x^2/2-x^3/3+3+pi^3/192-pi^2/32$

\0/ here's our answer !

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What is $f (x) = \int x - x^{2} sec x d x$ $f(x) = int x-x^2secx dx$ if $f (\frac{π}{4}) = 3$ $f(pi/4)=3$ ?

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What is $f (x) = \int x - x^{2} sec x d x$ $f(x) = int x-x^2secx dx$ if $f (\frac{π}{4}) = 3$ $f(pi/4)=3$ ?