i need to find the are trapped between the graphs of(adsbygoogle = window.adsbygoogle || []).push({});

y=-x^{3}

y=arctg[tex]\sqrt{x}[/tex]

x=2

x=1

y=arctg[tex]\sqrt{x}[/tex] will be my top function so the area will be

[tex]\int[/tex]arctg[tex]\sqrt{x}[/tex]-(-x^{3})dx from 1 to 2

in order to to this i can split the integral up and get

[tex]\int[/tex]arctg[tex]\sqrt{x}[/tex]dx -[tex]\int[/tex]-x^{3}dx both 1-2

|[tex]\int[/tex]-x^{3}dx| (1-2) is 3.75 with a simple table integral

but i dont know how to integrate the arctg

what i think could work is...

arctg[tex]\sqrt{x}[/tex]=t

tg(t)=[tex]\sqrt{x}[/tex]

[tex]\int[/tex]tdx while dt=dx/1+x^{2}

[tex]\int[/tex]t(1+x^{4})dt

=[tex]\int[/tex]t(1+tg^{4}t)dt

=[tex]\int[/tex]tdt+[tex]\int[/tex](tg^{4}t)dt

another option

[tex]\int[/tex]t(1+x^{4})dt

=1/2[tex]\int[/tex](1+tg^{4}t)dt^{2}

=0.5[tex]\int[/tex]dt^{2}+0.5[tex]\int[/tex](tg^{4}t)dt^{2}

sort of feels like im getting lost in it around here,,, any ideas??

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# Homework Help: Space between these functions of x

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