∫(1+4x2)^1/2 when x runs from 0 to 2

[lude1]

Homework Statement

∫(1+4x²)^1/2 when x runs from 0 to 2.

The answer is 4.647

Homework Equations

The Attempt at a Solution

I tried u substitution, giving me

u = 1+4x²
du = 8x​

where 8 can be pulled out as a constant. But I still have x left over. I'm sure I'm doing something silly or forgetting something basic, cause I'm pretty sure this is suppose to come to me fairly easy, especially since school is almost over...

 

[vela]

Try a trig substitution. The simple one you tried won't work because of that extra factor of x.

 

[lude1]

But how would you turn it into a trig substitution problem if the radical is not on the bottom of a fraction?

 

[Mark44]

Homework Statement

∫(1+4x²)^1/2 when x runs from 0 to 2.

The answer is 4.647

Homework Equations

The Attempt at a Solution

I tried u substitution, giving me

u = 1+4x²
du = 8x​

du = 8x dx

You omitted dx in your original integral. It is crucial to include the differential, especially when using trig substitution.

After you do a few of these types of problems you will probably start to realize that an ordinary substitution is not going to work at all. The reason for this is a vela already said - you are missing the x factor needed to get du, and there isn't anything you can do to get it.

where 8 can be pulled out as a constant. But I still have x left over. I'm sure I'm doing something silly or forgetting something basic, cause I'm pretty sure this is suppose to come to me fairly easy, especially since school is almost over...

 

[vela]

But how would you turn it into a trig substitution problem if the radical is not on the bottom of a fraction?

Why does it need to be on the bottom?