Calculus II Quest!!!!!!!!!!!!!!!!!!!!!!!

Question

a) Compute the area of the bounded region enclosed by the curve y=e^x, the line y=12, and the y-axis

b) How does this area compare with the value of the integral

∫121lnxdx? Explain your answer. (Please include a picture.)

 

Answer 1

y=e^x and y=12

e^x=12

x=ln12

limits are 0 to ln 12

A=Integrate ∫(12 - e^x)dx from 0 to ln 12.

   =(12x-e^x)from 0 to ln 12.

plug into limits

12 ln 12 - e^(ln 12) - (0 - e^0)

= 12 ln 12 - e^(ln 12) + 1

= 12 ln 12 - 12 + 1

  = 12 ln 12 - 11