Sorry, do you mean ?
I am new to this forum..so hello everyone! I am a student at UCD and sadly they make me take Calculus, even though I am a Political Science major...So please help me, I do not know if I did this right....
Find the Integral
(x + cos x) sin xdx the intervals are 0 and pi/2
My answer: [(sin x )^2]/2 + C...which is then .5-0 and then .5
Is this right?
Thank you so much!
So, you want to find:
You can go ahead and distribute the sin(x):
Now, you can split the integral:
Let's go ahead and do the second integral:
This can be solved with simple substitution:
Now we redo the limits in terms of u:
Our new integral is:
Now, we have to go back to the first integral:
We have to use parts:
Now, we have a complete integral:
Since the first term is gone, which leaves the second term, which is:
<--- Cancelled the negatives
So, the total is:
You can't make a direct substitution quite yet. Distribute the sine term throughout the parenthesis to get this:
Recall that .
We now have the following integral:
You will need to apply integration by parts to the first integral, and directly integrate the second.
Integration by parts : .
let and .
Now we have:
Since we're dealing with definite integrals, we don't need the .
Now, we have the following:
Evaluating, we get:
Hope this makes sense! If you want me to clarify, let me know!