Problem 6
Question
Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your result. $$ \int_{2}^{7} 3 d v $$
Step-by-Step Solution
Verified Answer
The value of the definite integral is 15.
1Step 1: 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.
2Step 2: 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 \(b = 7\).
3Step 3: Perform Calculation
Substitute the values into the formula to find the value of the integral. This gives \(3 * (7 - 2)\).
4Step 4: Find the Answer
The arithmetic operation yields 15. This is the solution to the definite integral.
Other exercises in this chapter
Problem 6
Find the integral. $$ \int \frac{x^{4}-1}{x^{2}+1} d x $$
View solution Problem 6
In Exercises 3-8, evaluate the definite integral by the limit definition. $$ \int_{1}^{3} 3 x^{2} d x $$
View solution Problem 6
Complete the table by identifying \(u\) and \(d u\) for the integral. $$ \int f(g(x)) g^{\prime}(x) d x \quad \underline{u=g(x)} \quad \underline{d u=g^{\prime}
View solution Problem 6
Find the indefinite integral. $$ \int \frac{x}{\sqrt{9-x^{2}}} d x $$
View solution