Find the area of the region under the graph of the function on the interval .

Question

Find the area of the region under the graph of the function  on the interval  .

Quizplus · Accepted Answer

To find the area under the curve, we need to integrate the function with respect to x from 0 to 1:

∫₀¹ 11e^(−8x−3) dx

We can use integration by substitution, where u = −8x − 3, du/dx = −8, and dx = −(1/8) du:

∫₋₃⁻⁰ 11e^u (−1/8) du

= (−11/8) ∫₋₃⁻⁰ e^u du

= (−11/8) [e^u]₋₃⁻⁰

= (−11/8) (e⁰ − e^₋₃)

= (11/8) (e^₋₃ − 1)

The correct answer is hence (C).

Find the Area of the Region Under the Graph of the Function