find formula for the function represented by the integrals.

Question

anonymous · Answer

attachment

seascorpion1 · Answer

Use the integral sum rule to get: $$\int\limits_{\sin( \theta)}^{4}5tdt+\int\limits_{\sin( \theta)}^{4}9dt$$

anonymous · Answer

Okay but what do you do with sin(theta) once you do the antiderivitve

seascorpion1 · Answer

Can you show me your workings?

anonymous · Answer

I got 5t^2/2 +9t and I don't know how to plug in sin theta

anonymous · Answer

can you just finish the problem haha and I'll see how you use it :)

seascorpion1 · Answer

evaluate that at 4 and then subtract it evaluated at sin theta

anonymous · Answer

How do you evaluate at sin theta though?

seascorpion1 · Answer

Let t=sin theta

anonymous · Answer

Im still confused

anonymous · Answer

Can you just evaluate it for me

seascorpion1 · Answer

$$\frac{5}{2}(\sin(\theta))^2+9\sin(\theta)$$

seascorpion1 · Answer

Have you solved it yet?

anonymous · Answer

I don't know how to solve it with theta

anonymous · Answer

thats where I'm confused

anonymous · Answer

Can you just answer it for me

seascorpion1 · Answer

$$\frac{5}{2}*4^2+9*4-(\frac{5}{2}\sin^2(\theta)+9\sin(\theta))$$

seascorpion1 · Answer

Have you solved it yet?

anonymous · Answer

I don't know what to plug in for sintheta

anonymous · Answer

Can you just please give me the answer

seascorpion1 · Answer

In order to solve the integral you need to plug something in for t therefore you should let t=sin theta. The equation you came up with above is correct so you now need to make the substitution with the sin theta (i.e. replace the t with the sin theta) then you should have solved it. Let me know how you get on.

anonymous · Answer

figured it out.  Thanks!

seascorpion1 · Answer

You're welcome!