Can anyone please help
An engineering process is tested over a period of 60secs. the equation can be given by y=e(to the power)0.06t.
a) Use numerical integration with 10 second itervals to find the area.
b) use integral calculus to find the area.
c) Compare your answers to part (a) and (b), stating which is more accurate and giving your reasons.
Thanks
Headbazza
Hello headbazza
The simplest method of doing a numerical integration is to use the Trapezium Rule.
Imagine the area under the curve divided vertically into strips of equal width , with the curve replaced by straight line segments. Then the area is approximately the same as the sum of the areas of the trapezia; which is:, where are the equally spaced values of .So, to use this formula in your question, you'll work out , and then:
Area =Take care with the calculation, and it should be very straightforward.
For (b):AreaFor (c), the answer to (b) will be more accurate because in (a) the curve has been replaced by straight line segments joining the ordinates at .
Grandad