Thread: Finding the area between curve, tangent and y axis.

1. Finding the area between curve, tangent and y axis.

Having difficulties solving the following question part c.

Q15
a)sketch the curve of e^x+2
b)Find the equation of the tangent at x=-2. I worked this out to be y=x+3
c)find the area between the curve, tangent and y axis.

-i Know that the tangent equation x+3 and e^x+2 intersect at x=-2 and that the area bounded by the y axis should be between the two functions y intercepts which are 3 and e^2.

2. Re: Finding the area between curve, tangent and y axis.

I guess the function is: $y=e^{x+2}$
b) right!
c) Have you learned to integrate? ...

3. Re: Finding the area between curve, tangent and y axis.

Yes i sure have learned to integrate. For 'in between the curves' would i find the integral from 0 to -2 of e^x+2 - x+3? +(y axis) integral from e^2 to 3 of e^x+2 - x+3........

4. Re: Finding the area between curve, tangent and y axis.

(Useful is to graph the functions, have you done that?)
You've to calculate:
$\int_{-2}^{0} [e^{x+2}-(x+3)]dx$