2
2
dx
x(lnx)
∞
∫
1. Consider the integral ∫ Arctan x dx.
(a) Use the integration by parts formula on this integral. Clearly
indicate your choice for u and v, as well as their differentials, du
and dv
(b) Using part (a), complete the integration.
(c) Check your answer (how?)
2. Is the following improper integral convergent or divergent?
If it is convergent, find the value of the integral.
3. Consider curve given by x = t2, y = t3 – 3t
(a) Find the equations of all horizontal tangent lines to the
curve.
(b) Find an expression for the second derivative, 2
2
dy
dx .
4. Consider the curve given parametrically by x = et, y = In t.
(a) Write an expression for the differential of arc length, ds .
(b) Set up an integral that gives the length of the
curve from t – 1 to t = 2.
