Solve the problem. -Find the area between y = (x - 2)e^x and the x-axis from x = 2 to x = 6. A) e⁶ + e² B) 3e⁶ C) 3e⁶ + e² D) e⁶ - e²

Question

Quizplus · Accepted Answer

The area between the curve and the x-axis is given by the integral of the function from x = 2 to x = 6.$$\int_2^6 (x - 2)e^x dx$$Using integration by parts, we get:$$= (x - 2)e^x \bigg|_2^6 - \int_2^6 e^x dx$$$$= (6 - 2)e^6 - (2 - 2)e^2 - e^x \bigg|_2^6$$$$= 4e^6 - e^2$$Therefore, the area between the curve and the x-axis is 3e⁶ + e².

Solve the Problem. -Find the Area Between Y = (X - 2)ex and -

Solve the Problem. -Find the Area Between Y = (X - 2)e^x and -