Sketch the region enclosed by y = e^4x , y = e^7x , and x = 1 . Find the area of the region.

Answer 1

Area = ∫₀¹( e^7x -e^4x)dx = e^7x/7 -e^4x/4 |₀¹ =e⁷/7 - e⁴/4 = ( 4 e⁷ -7 e⁴ )/28 =(4386.5 - 382.2)/28= 143.01