3. Evaluate:

To evaluate the integral , we can use the substitution method. Let . Then, the derivative , or .

Now, we also need to express in terms of :
Since , we have .
However, for simplicity, we can express as , which suggests that further simplification might be necessary.

Now substitute limits: when , ; when , .

Putting it all together:

To solve , expand it:

Calculating these defined terms:
At :

At :

Now evaluate:
Calculate values and subtract the lower limit evaluation from the upper limit evaluation. The valid computations give the final result for the initial integral requested. In total, through careful substitutions and integrations, we reach a summative answer of the mentioned defined function’s bounds.

Finally, integrate those respective limits for a precision on those fractional values.

Thus, the complete problem leads to:

This will yield the final numerical evaluation revealing insightful connectivity via function transformation and limits.