# Thread: area under exponential function

1. ## area under exponential function

Using simultaneous equations I have worked out my exponential function for the top left hand corner of the attached picture to be:

f(x) = 10.767 (1.346)^x

I need to find the area under this graph in the top left hand corner of the attached picture. I am need of some assistance please.

2. Originally Posted by Mr.Ree
Using simultaneous equations I have worked out my exponential function for the top left hand corner of the attached picture to be:

f(x) = 10.767 (1.346)^x

I need to find the area under this graph in the top left hand corner of the attached picture. I am need of some assistance please.
Area under $\displaystyle f(x)$ to the left of $\displaystyle x=u$ is:

$\displaystyle \int_0^u f(x) \;dx= 10.767 \int_0^u e^{x\ln(1.346)}\;dx$

................ $\displaystyle =\frac{10.767}{\ln(1.346)} \left[e^{x\ln(1.346)}\right]^u_0$

................ $\displaystyle =\frac{10.767}{\ln(1.346)} (1.346^u-1)$

or if you want the actual area shown in the figure (including the initial rectangular bit) you want:

$\displaystyle A=8+\int_1^8 f(x) \;dx=8+\frac{10.767}{\ln(1.346)} (1.346^8-1.346)$

CB