Evaluate the Integral

Problem

(∫_0^3)(√(,5)*d(x))

Solution

1. Identify the integrand, which is the constant value √(,5)

2. Apply the constant rule for integration, which states that (∫_^)(k*d(x))=k*x

3. Evaluate the definite integral by applying the Fundamental Theorem of Calculus at the boundaries 0 and 3

[√(,5)*x]30

4. Substitute the upper limit and subtract the evaluation of the lower limit.

√(,5)*(3)−√(,5)*(0)

5. Simplify the expression to find the final numerical value.

3√(,5)−0

Final Answer

(∫_0^3)(√(,5)*d(x))=3√(,5)

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