# Thread: Need help with 2 questions

1. ## Need help with 2 questions

1. Calculate the integrals of:

a*x*sin(bx) dx
and
(x^2)(sin^2(ax)) dx
where a and b are constants. hint: use double angle formula

2. consider the improper integral

integral from (2*sqrt(3)) to infiniti of: (24x^3)/(4+x^2)^(5/2) dx.
EDIT: Make an appropriate trigonometric substitution to convert into a proper integral. Hence determine its value.

Someone can help me with these please?

1. Calculate the integrals of:

a*x*sin(bx) dx

Mr F says: Use integration by parts.

and
(x^2)(sin^2(ax)) dx
where a and b are constants. hint: use double angle formula
Mr F says: $\displaystyle {\color{red}\sin^2 (ax) = \frac{1}{2} \left( 1 - \cos (2ax) \right)}$.

Hint 2: Use integration by parts (twice).

2. consider the improper integral

integral from (2*sqrt(3)) to infiniti of: (24x^3)/(4+x^2)^(5/2) dx.
EDIT: Make an appropriate trigonometric substitution to convert into a proper integral. Hence determine its value.

Mr F says: Substitute $\displaystyle {\color{red} x = 2 \tan t}$.

Someone can help me with these please?
Since you've been set these questions I'm assuming you've been taught integration by parts and that you know how to make a substitution.

If you need more help please show the working you've done and state exactly where you're stuck.

By the way - bumping and begging for help is against the forum rules that you agreed to when you became a member.

3. Sorry about the nagging, im just getting desperate, lol. Anyways thanks, I will work on what you said and see where I get from there.