Find the total area enclosed by the graph of y=(e^sinx)*(cosx) and the x-axis from x=0 to x=pi
I got .0563331993 but when I checked it graphically I got 3.22765
You need to integrate the y function from 0 to pi. The indefinite integral is e^sinx
Its value is 1 at x=pi and 1 at x = 0.
The definite integral is therefore zero.
The area from 0 to pi/2 is the same as the area from pi/2 to pi, but the sign changes when the curve goes below the x axis.
if you don't count area below the x axis as negative, the area you should get is 2(e -1) = 3.437
Yep, the graph looks kind of like a squiggly line with equal area above and below the X axis. If you're looking for the total enclosed area, you want to multiply the integral from zero to pi/2 by 2. If you're actually taking the integral though (you're concerned about the sign of the area not just the absolute value), you would get zero. Your calculator will report something like .0563331993 because it is approximating the answer.
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To find the total area enclosed by the graph of the function y = (e^sinx)*(cosx) and the x-axis from x = 0 to x = pi, we can use the definite integral.
First, let's set up the integral:
∫[0, π] (e^sinx)*(cosx) dx
To find the integral, we can use a numerical integration method such as a calculator or software, or we can approximate it using a small step size.
If you got the answer 0.0563331993, it seems there might be a mistake in your calculation. The correct answer using numerical integration methods should be closer to the value you obtained graphically, which is 3.22765.
I suggest you double-check your calculations or try using a more precise method of numerical integration to get a more accurate result.