Question

evaluate the integral
int_{5}^{8} 8 , dx
int_{5}^{8} 8 , dx = (simplify your answer.)

Explanation:

Step1: Apply the integral rule for a constant

The integral of a constant \(k\) with respect to \(x\) is \(kx + C\). For \(\int 8dx\), the antiderivative is \(8x\).

Step2: Use the fundamental theorem of calculus

The fundamental theorem of calculus states that \(\int_{a}^{b}f(x)dx=F(b)-F(a)\), where \(F(x)\) is the antiderivative of \(f(x)\). Here, \(a = 5\), \(b = 8\), and \(F(x)=8x\). So, \(F(8)-F(5)=8\times8 - 8\times5\).

Step3: Simplify the expression

$$
LATEXBLOCK0
$$

Answer:

\(24\)