Evaluate the definite integral.
$\int_{0}^{1} \sqrt{5 x + 5} d x$

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Answer

Final Answer: The definite integral of $\sqrt{5 x + 5}$ from 0 to 1 is approximately $2.73$ .

Steps

Step 1 ：We are given the definite integral $\int_{0}^{1} \sqrt{5 x + 5} d x$ .

Step 2 ：To solve this, we can use the power rule for integration, which states that the integral of $x^{n} d x$ is $(1 / (n + 1)) x^{(} n + 1)$ .

Step 3 ：However, before we can apply the power rule, we need to rewrite the function in a form that allows us to do so.

Step 4 ：We can rewrite $\sqrt{5 x + 5}$ as $(5 x + 5)^{1 / 2}$ .

Step 5 ：By evaluating the integral, we find that the value is approximately 2.73.

Step 6 ：Final Answer: The definite integral of $\sqrt{5 x + 5}$ from 0 to 1 is approximately $2.73$ .