Question

find the area under the given curve over the indicated interval
( y = 2x ), ( 2, 8 )

the area under the curve is \\( \square \\) (simplify your answer.)

Explanation:

Step1: Identify the integral formula

The area under \(y = 2x\) from \(x=0\) to \(x=7\) is \(\int_{0}^{7} 2x dx\).

Step2: Compute the integral

Antiderivative of \(2x\) is \(x^2\). Evaluate from 0 to7: \(7^2 - 0^2 = 49\).

Answer:

49