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suppose ,that we are going to find are of $x*y=4$ bounded by $x=1$ and $x=4$ and $y=0$

generaly as i know are of function $y=f(x)$ bounded by $x=a$ and $x=b$ is given by

$A=\int(f(x)), x=a,x=b $; so in this case $y=4/x$ it's integral would be $4*ln(x)$,now if we put variables we will get $4*ln(4)-4*ln(1)$=$5.545-4*0=5.545$ but because this is bounded by $y=0$,is there any place where i should use this?for example in intersection or anything else?thanks guys

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Draw a picture, and think about the region you are asked to find the area of. It is below (or on) $y=4/x$, above (or on) the $x$-axis ($y=0)$, from $x=1$ to $x=4$. Totally standard area problem. You got the right answer. The reason you were unsure is probably that you looked first for a formula, and not a picture. – André Nicolas May 4 '12 at 18:33
you are right @ André Nicolas thanks for advice – dato datuashvili May 4 '12 at 18:55
up vote 3 down vote accepted

The area under $xy=4$ (i.e. bounded below by $y=0$) for $x\in[1,4]$ would be $$\int_1^4\frac4xdx=4\,\Bigl.\ln x\Bigr|_1^4=4\Bigl(\ln 4-\ln 0\Bigr)=4\ln 4\approx5.545177444$$

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aaa sorry i have put 3 instead of 4,sorry – dato datuashvili May 4 '12 at 18:54

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