# How do I evaluate #int_1^4sqrt(t) \(5 + 2 t) dt#?

I would expand the argument as:

I can now separate the integrals, as:

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To evaluate ( \int_{1}^{4} \sqrt{t}(5 + 2t) , dt ), you would first distribute the square root term into the polynomial, then integrate each term separately. The integral would yield ( \frac{32}{3}\sqrt{4} - \frac{4}{3}\sqrt{1} + \frac{5}{3}(4^{\frac{3}{2}} - 1) ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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