Integrate:
a)
answer is , where does 1/2 come from??
b)
answer is , what did I do wrong?
When you're putting substitutions on integral you're not subst. everything, you're working with both x and u. When you substitute something with u, you have to express everthing inside of integral with u.
In that case in a) after sub. the integral would be. Here substitute again
so the integral will be
The same mistake in part b).
Because we want to solve it by substitution...That is the correct substitution because when you differentiate it becomes
so now the expression under integral you'll sub. with . When you finish the integral you have to get back the substitutions.
In part b). after doing those substitutions you'll have
now the integral will be
now I believe you can finish it.