Saturday, July 29, 2017

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 10

Evaluate sin1xdx
If we let u=sin1x and dv=dx, then
du=11x2dx and v=dx=x

So,
sin1xdx=uvvdu=xsin1xx1x2dx
To evaluate x1x2dx we let u1=1x2, then du1=2xdx


Then,

x1x2dx=du12u1=12u121du1=12[u12112]=(u1)12+c=(1x2)12+c


Therefore,

sin1xdx=xsin1x[(1x2)12]+c=xsin1x+(1x2)12+c

No comments:

Post a Comment

Why is the fact that the Americans are helping the Russians important?

In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...