Evaluate the Integral

Problem

(∫_2^4)(3*d(x))

Solution

1. Identify the integrand and the limits of integration. The integrand is the constant function ƒ(x)=3 and the limits are a=2 and b=4

2. Apply the Power Rule for integration. The integral of a constant k with respect to x is k*x

3. Evaluate the definite integral using the Fundamental Theorem of Calculus by subtracting the value of the antiderivative at the lower limit from the value at the upper limit.

[3*x]42

4. Substitute the values of the limits into the expression.

3*(4)−3*(2)

5. Simplify the arithmetic to find the final value.

12−6=6

Final Answer

(∫_2^4)(3*d(x))=6

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