I need some help figuring out what this notation means. I posted the problem and beneath it is some of the information I found about it
integral_{x=0 to pi/2} sin(x)cos(x)/[x+1] dx
first combine the sin and cos to get:
integral_{x=0 to pi/2} sin(x)cos(x)/[x+1] dx =
....................... integral_{x=0 to pi/2} sin(2x)/[2x+2] dx
Now change the variable of integration to u = 2x+2, to get:
integral_{x=0 to pi/2} sin(x)cos(x)/[x+1] dx =
....................... integral_{u=2 to pi+2} (1/2) sin(u-2)/u du
....................... integral_{u=2 to pi+2} (1/2) [sin(u)cos(2)-cos(u)sin(2)]/u du
and the result should now follow from the definitions of the sin and cosin
integrals Si and Ci.
RonL
added in explanation: you also need that for a sufficiently well behaved function:
integral_{u=a to b} f(u) du = integral_{u=0 to b} f(u) du - integral_{u=0 to a} f(u) du