Quiz Question 2

Evening Everyone,

I’m having some problems with the answer to number two and I’m hoping someone can clear things up.

\int_0^1f(2x+1)dx

From here we find our u-sub and dx values which I found to be;

u=2x+1
dx=\frac{1}{2}du

After finding our new bounds we can substitute u values and set our equation equal to 8 and get;

\int_1^3f(u)\frac{1}{2}du=8 or \frac{1}{2}\int_1^3f(u)du=8

To get our final answer, and this is where I’m confused, I divided by \frac{1}{2} and got a final answer of 16.

\frac{\frac{1}{2}\int_1^3f(u)du}{\frac{1}{2}}=\frac{8}{\frac{1}{2}}= \int_1^3f(u)du=16

Could someone explain why this isn’t the correct way to go about this?

Thanks!

You found dx = \frac{1}{2}du correctly but made your mistake right after that when you conclude that

That can’t be correct because you are given that

What you’re actually really close to showing is that

Thus, the answer is \frac{1}{2}\times8 or 4.

Thank you that makes sense now!