f(x) = e^2x

Let F(x) = intg f(x)

==> F(x) = intg e^2x dx

= e^2x/2 + c

==> F(x) = 2^2x/2 + C

Now the difinite integral from x= 0 to x= 2 is the area between the f(x) and x= 0 and x= 2:

A = F(2)...

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f(x) = e^2x

Let F(x) = intg f(x)

==> F(x) = intg e^2x dx

= e^2x/2 + c

==> F(x) = 2^2x/2 + C

Now the difinite integral from x= 0 to x= 2 is the area between the f(x) and x= 0 and x= 2:

A = F(2) - F(0)

=(e^2*2/2 + c ) - (e^2*0 / 2 + c)

= (e^4)/2 - e^0/2

= (e^4)/2 - 1/2

= (e^4 - 1)/2

**==> The definite integral is (e^4 - 1)/2**