Final answer:
The question involves evaluating the integral of a square root function, which suggests a strategy of completing the square and using basic antiderivative rules followed by adding the constant of integration.
Step-by-step explanation:
We have been asked to evaluate the integral of the function √(21+4x − x²). This problem is a calculus problem that involves finding the antiderivative of a square root function, which may require substitution to simplify.
The integral resembles the form of an integral over a quadratic, which can often be solved by completing the square. In this case, we recognize that the expression under the root can be rewritten as:
√(21 + 4x - x²) = √((5 - x)^2)
Now, we take the integral:
∫ √((5 - x)^2) dx
The solution involves a straightforward antiderivative of a square root of a square function. Finally, don't forget to add the constant of integration 'C'.