How would I use the Comparison Test in calculus to solve the integral #(cos(4x) +3) / (3x^3 + 1)# from 1 to infinity?
1 Answer
Sep 12, 2015
I'm not sure what you mean by "solve".
Explanation:
By comparison, we can see that the integral converges.
graph{(y-100((cos (4x)+3)/(3x^3+1)))(y-((400)/(3x^3+1)))=0 [0.33, 11.433, -0.75, 4.8]}
(Both multiplied by 100 for clarity of relationship.)
And
So
graph{(y-100((cos (4x)+3)/(3x^3+1)))(y-((400)/(x^3)))=0 [0.2, 17.985, -1.124, 7.766]}
(Again multiplied by 100 for clarity.)
And it is not difficult to see that
So