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Chapter 4: Problem 6

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your result. $$ \int_{2}^{7} 3 d v $$

Short Answer

Expert verified
The value of the definite integral is 15.

Step by step solution

01

Identify Function Type

The problem presents an algebraic function in the form of a constant. Recognizing this informs that the integral of a constant function, \(3\), over an interval \([2,7]\) would correspond to the area under the line between these limits.
02

Apply the Fundamental Theorem of Calculus

Using the Fundamental Theorem of Calculus, the integral of a constant function \(c\) from \(a\) to \(b\) is simply \(c(b-a)\). Here, \(c = 3\), \(a = 2\), and \(b = 7\).
03

Perform Calculation

Substitute the values into the formula to find the value of the integral. This gives \(3 * (7 - 2)\).
04

Find the Answer

The arithmetic operation yields 15. This is the solution to the definite integral.

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