Evaluate a definite integral by rewriting a radical as a fractional exponent, finding the antiderivative, and applying the Fundamental Theorem of Calculus.

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Evaluating a Definite Integral with a Radical and a Polynomial Term

The definite integral warmup

Evaluate \( \int_{4}^{5} \left( \frac{2}{\sqrt{x}} - x \right) dx \).

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What you need first

fractional exponents
power rule for integration
evaluating algebraic expressions

What this problem tests

Tests the ability to rewrite expressions with fractional exponents, apply the power rule for integration, and correctly evaluate a definite integral at its bounds.

This is a standard introductory calculus problem testing basic integration techniques and the evaluation of definite integrals.

Evaluating a Definite Integral with a Radical and a Polynomial Term

What you need first

What this problem tests

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