266
CHAPTER 32
32.50
Evaluate
32.51
Evaluate
(The same result is obtained from Problem 29.45.)
32.52
Evaluate
There is a discontinuity at x = 1. Then
32.53 Evaluate
cot x dx.
32.54 Evaluate
for *>!. Hence by Problem 32.9,
tan ' x dx = +«.
tan
l x>ir/4
32.55
Find the area between the curves y = l/x and y = l/(x + l) to the right of the line .v'= 1.
The area
32.56
Find the area in the first quadrant under the curve y - 1 /(x
2 + 6x + 10).
Problems 32.57-32.60 refer to the Laplace transform L{f} = ^ e'
s 'f(t) dt of a function/(/), where s>0.
(L{f} may not be defined at some or all s >0.) It is assumed that lim e~"f(t) = 0.
32.57 Calculate L(t}.
(Here, the integration was performed by parts: u = t, dv = e
s< dt.) Thus, L{t} = \ls
2 .
tan -1 x dx.