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

Answer

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Answer

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

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 \(x^n dx\) 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 \(\sqrt{5x+5}\) as \((5x+5)^{1/2}\).

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

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