Fundamental Theorem of Calculus
The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieve..
First Fundamental Theorem of Integral Calculus
Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined by th..
Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined by th.. One of the best CALCULUS problems I have ever seen using calculus. Shows that in fact it is useful in life!
I made this video while I was supposed to actually be studying calculus. Ooooh, the irony. When I'm not making dumb videos (which is most of the time), I'm making music. Check me out! www.myspace.com
Question : Calculus was orginally invented to solve two problems that had concerned mathematicians for centuries. What were they?
Answer : 1. Differentiation, the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behaviour of functions. 2. Integration, the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced... More from Yahoo Answers
Answer : 1. Differentiation, the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behaviour of functions. 2. Integration, the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced... More from Yahoo Answers
Question : I am interested in some challenging calc problems that require some creativity to solve, a stretching of the mind, something like that. Perhaps an insight or two here and there. Such problems were far and few in my Calc I textbook and as I independently study Calc II I am also not finding many of those. The study of calculus has so far been much fun than the study of algebra where one could easily find hundreds of challenging problems on the internet.
Answer : integrate sq rt(tan(x)) Here are some hints: it requires 6 separate uses of u-substitution and two separate uses of partial fractions expansion. I'll be happy to send you the solution if you want. Calculus isn't that interesting until you take vector calculus, then you start to see a lot of ideas come together. Find the area under the curve 1/(2 + cos(x)) from 0 x /2.. More from Yahoo Answers
Answer : integrate sq rt(tan(x)) Here are some hints: it requires 6 separate uses of u-substitution and two separate uses of partial fractions expansion. I'll be happy to send you the solution if you want. Calculus isn't that interesting until you take vector calculus, then you start to see a lot of ideas come together. Find the area under the curve 1/(2 + cos(x)) from 0 x /2.. More from Yahoo Answers
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