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Question about this midpoint approximation problem (Calculus)?
In our online homework, I've stumbled across a problem which seems very tedious to solve out even with a calculator available and I'm wondering if there's a possible shortcut.
The problem is the integral of sin(pi * x) (dx) with the limits of integration being 3 and 6.
The subinterval is n = 25... which is where I find it to be very tedious.
(6-3)/25 = 3/25 = delta X which tells me that the x points are
75/25, 78/25, 81/25 and so on. It'd be very annoying to plug in the midpoint of each set of plots into the function...
I do not need the problem solved out. I did eventually crank it out and got it correct but the entire process just to solve one homework problem seems ridiculous.
2 Answers
- 4 years ago
The process is tedious, especially for an elementary integral, but that's the point. These exercises are designed to show you the theory behind integration as well as the way you can solve non-elementary integrals later. For instance, how would you integrate e^(-x^2)? e^(-x) can be integrated quite easily, but e^(-x^2) or e^(-x^3) or the like is much more difficult. But they can be managed with these techniques.
