Asked by Kayla
Find the area bounded by y=1/x, the x-axis and the lines y=1 and x=4
Answers
Answered by
Reiny
I made a sketch.
I see a square from x=0 to x=1, then a curved region from x=1 to x=16, bounded at the top by y = 1/x
the area of the square is 1
so the area from x=1 to x=16
= ∫ 1/x dx from 1 to 16
= lnx from 1 to 16
= ln16 - ln1
= ln16
total area = 1 + ln16
I see a square from x=0 to x=1, then a curved region from x=1 to x=16, bounded at the top by y = 1/x
the area of the square is 1
so the area from x=1 to x=16
= ∫ 1/x dx from 1 to 16
= lnx from 1 to 16
= ln16 - ln1
= ln16
total area = 1 + ln16
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