The trick here is to use an appropriate substitution. Let u=a^3.
Then du/da=3a^2, and du=3a^2da.
We can now make two key substitutions: In (3a^2)da/(1+a^6), replace 3a^2 by du and a^6 by u^2.
Then we have the integral of du/(1+u^2).
Integrating, we get arctan u + c. Substituting a^3 for u, the final result (the integral in question) is arctan a^3 + c.
Check this by differentiation. if you find the derivative with respect to a of arctan a^3 + c, you MUST obtain the result 3a^2/(1+a^6).
20 and 2/3 is correct, I think
It’s (-5,-2) You can figure this out by going to the left 5 times which is negative so -5. And going down on a graph is negative so down 1 means -1 so you add the -1 to the other negative one and now you have -2. So that is how you get the answer.
Hi there, we are going to set up a porportion. 640 miles/25 hours ÷ 25/25. That would equal 25.6 miles/1 hour. Therefore, the answer is 25.6 miles per hour.
Answer:
11/12
Step-by-step explanation:
1/4+2/3
1/4×3/3+2/3×4/4
3/12+8/12
