Please find the area between the xaxis and fx over each of t

Please find the area between the x-axis and f(x) over each of the intervals. (All the area, are above x-axis; therefore you do not, need consider the sigh.)

Solution

(1) A = integral (1 + exp(-x)) dx from 0 to 4

= [ x - exp(-x)] from 0 to 4

= 4 - (e^-4 - 1)

= 5 - e^-4

(2) A = integral (2x + 3)⁶ dx from x=-1.5 to 0

= (1/14) (2x + 3)⁷ from x=-1.5 to 0

= (1/14) [3⁷ ]

= 2187/14