weve been in the class for almost 2months now and where going to start chpt4
today we learned about hyperbolic trig functions
and previously we did related rates
will we get to integration soon?
btw what exactly is integration
today we learned about hyperbolic trig functions
and previously we did related rates
will we get to integration soon?
btw what exactly is integration
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Doubtful. Usually calculus is a four part series: differential, integral, multivariate, and vector. Just like learning to multiply before you divide you need to learn how to differentiate before you integrate. Because differentiate is much easier (mechanically, and some would argue conceptually), the extra time is taken to introduce functions which many people have never seen before, like the hyperbolic functions, as well as applications of the derivative, like related rates.
Integration is essentially the continuous analogy of summation. A summation is taken over integers, e.g. ∑{n = 1,10} n. Integrals are taken over the reals, e.g. ∫[0,1] x dx. The most common application (this appears in the definition) of the integral is finding the area under a curve and above the x-axis. This comes up a lot in probability. This idea can also be used to find average values of the function over an interval.
For more about the mechanics, definition, and application see:
http://mathworld.wolfram.com/Integral.ht…
http://www.khanacademy.org/ (search for "integral" or navigate to the calculus section)
Integration is essentially the continuous analogy of summation. A summation is taken over integers, e.g. ∑{n = 1,10} n. Integrals are taken over the reals, e.g. ∫[0,1] x dx. The most common application (this appears in the definition) of the integral is finding the area under a curve and above the x-axis. This comes up a lot in probability. This idea can also be used to find average values of the function over an interval.
For more about the mechanics, definition, and application see:
http://mathworld.wolfram.com/Integral.ht…
http://www.khanacademy.org/ (search for "integral" or navigate to the calculus section)
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In my high school calculus class, we covered a variety of topics including both differentiation and integration. However, in my university calculus classes, Calculus 1 was primarily differential calculus, and we didn't do integration at all. Calculus 2 was integral calculus and therefore focused on integration.
Integration is essentially a method of calculating the area under the curve described by a function, or the area between two such curves, or the volume of the solid created when a curve is rotated around an axis. In many ways, it is the opposite of differentiation.
Integration is essentially a method of calculating the area under the curve described by a function, or the area between two such curves, or the volume of the solid created when a curve is rotated around an axis. In many ways, it is the opposite of differentiation.