let r be the region in the first quadrant between two graphs. the volume of

B

Brica

New member
the solid is?? calc help? Let R be the region in the first quadrant between the graphs of y = e^(-3x), y=sin(x), and the y-axis. The volume of the solid that results when R is revolved about the x-axis is

a) 0.098

b) 0.132

c) 0.308

d) 0.416

e) 0.831

could you show me how you got your answer?
 
This is a washer, e^(-3x) and sin(x) intersects at x = 0.354 and both function intersections the y axis at x = 0

Look at it from a graph if you don't understand

So our limits of integration is 0 and 0.354

The upper function is e^(-3x) and the lower function is sin(x)

pi integrate [ [e^(-3x)]^2 - (sin(x))^2 ] dx (from 0 to 0.354)

The algebra gets a bit messy, so use a calculator to finish the job.

Answer = 0.4157, which is roughly 0.416 and therefore is d)
 
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