Posted by **Naseba** on Wednesday, April 4, 2012 at 10:59pm.

Let R be the region in the first quadrant that is enclosed by the graph of y = tanx, the x-axis, and the line x = π/3

h. Find the area of R

i. Find the volume of the solid formed by revolving R about the x-axis

- calculus -
**Steve**, Thursday, April 5, 2012 at 11:09am
what's the problem?

A = ∫[0,pi/3] tanx dx

integrating tanx is easy, since

tanx = sinx/cosx = -d(cosx)/cosx

∫tanx dx = -ln(cosx)

A = -ln(cosx) [0,pi/3]

= -ln(cos pi/3) + ln(cos 0)

= -ln(1/2) + ln(1)

= ln2

v = ∫[0,pi/3] pi*r^2 dx

= pi*∫[0,pi/3] tan^2x dx

= pi*∫[0,pi/3](sec^2x - 1) dx

= pi*(tanx - x) [0,pi/3]

. . .

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