Asked by Venne
Sketch the region bounded by the graphs of the algebraic functions & find the area of the region:
f(x)=10/x, x=0 , y=2, y=10
I started idk how to keep going y = 10/x for x -->x = 10/y
f(x)=10/x, x=0 , y=2, y=10
I started idk how to keep going y = 10/x for x -->x = 10/y
Answers
Answered by
Steve
Huh?
Just sketch the graph. It's a smooth curve coming down from far up the y-axis, bending smoothly at about x=3, and continuing on out, getting closer to the x-axis. Any grapher can show this.
Your region of interest is a small triangular-ish strip beside the y-axis between y=2 and y=10.
So, the area is the Integral of 10/x from x=10/10 to x=10/2
Intgeral of 10/x dx is just 10 lnx
So, evaluate 10lnx[1,5]
= 10(ln5 - ln1] = 10ln5 = 16.09
Just sketch the graph. It's a smooth curve coming down from far up the y-axis, bending smoothly at about x=3, and continuing on out, getting closer to the x-axis. Any grapher can show this.
Your region of interest is a small triangular-ish strip beside the y-axis between y=2 and y=10.
So, the area is the Integral of 10/x from x=10/10 to x=10/2
Intgeral of 10/x dx is just 10 lnx
So, evaluate 10lnx[1,5]
= 10(ln5 - ln1] = 10ln5 = 16.09