SOLUTION: two questions and answers: a) integrate 3^x answer: 3^x/In(3) b) find the exact area enclosed by the curve y=e^3x - 2, the x-axis and the lines x=0 and x=1 answer: 4In(2)/3 + e

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: two questions and answers: a) integrate 3^x answer: 3^x/In(3) b) find the exact area enclosed by the curve y=e^3x - 2, the x-axis and the lines x=0 and x=1 answer: 4In(2)/3 + e      Log On


   



Question 758447: two questions and answers:
a) integrate 3^x
answer: 3^x/In(3)
b) find the exact area enclosed by the curve y=e^3x - 2, the x-axis and the lines x=0 and x=1
answer: 4In(2)/3 + e^3/3 - 3
my question is, how do you get to these answers? can you please show me step by step.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
two questions and answers:
a) integrate 3^x
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3%5Ex+=+e%5E%28x%2Aln%283%29%29
INT%28e%5E%28x%2Aln%283%29%29%29+=+e%5E%28x%2Aln%283%29%29%2Fln%283%29
= answer
answer: 3^x/In(3)
==============
b) find the exact area enclosed by the curve y=e^3x - 2, the x-axis and the lines x=0 and x=1
INT%28e%5E%283x%29+-+2%29+=+e%5E%283x%29%2F3+-+2x Ignore the constant of integration
INT%281%29+=+e%5E3%2F3+-+2
INT%280%29+=+1%2F3
=============
What is the exponent of e? 3x? or 3x-2?
answer: 4In(2)/3 + e^3/3 - 3 =~ 4.619375