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Mathematics 16 Online
OpenStudy (anonymous):

integration of [(x+ pi)^3+ cos^2 (x+3*pi)] dx from (-3pi/2) to (-pi/2)

OpenStudy (anonymous):

i

OpenStudy (anonymous):

\[\int\limits_{\frac{-3\pi}{2}}^{\frac{-\pi}{2}} [(x+ \pi)^3 + \cos^2(x+3\pi)]dx\]?

OpenStudy (anonymous):

i dont know why i can't open the equation editor..:-(

OpenStudy (anonymous):

is this the question?

OpenStudy (anonymous):

yup.. the Q isn't confusing you ryt?

OpenStudy (anonymous):

let me think about it first :)

OpenStudy (anonymous):

sure.. take your time.

OpenStudy (anonymous):

you can cut it down into the following:\[\int\limits_{\frac{-3\pi}{2}}^{\frac{-\pi}{2}}(x+\pi)^3 dx +\int\limits_{\frac{-3\pi}{2}}^{\frac{-\pi}{2}}\cos^2(x+3\pi)dx \] for the first part, expand the polynomial and integrate normally, and as for the second part, let u = x+3pi and integrate using the half angle formula for cos^2 u, which is in this case : \[\cos^2u = \frac{1}{2}(1+\cos2u)\] give it a try :)

OpenStudy (anonymous):

hey it worked! thanx!:-)

OpenStudy (anonymous):

np ^_^

OpenStudy (anonymous):

you did even need to expand the first bit\[\int\limits_{}^{} (ax+b)^n = (ax+b)^{n+1} / [a(n+1)] +C\] I cant manage to get a straight horizontal bar for fractions when working with the equation editor :|

OpenStudy (anonymous):

didnt*

OpenStudy (anonymous):

oh that expansion part jus worked out easy using a property of definite integrals.. \[\int\limits_{a}^{b} x dx = (b+a - x)dx\] plugging in the values of the question the whole thing comes out negative. thus adding them would yield zero. solving the trig part yields \[\pi/2\]

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