sorry, the parenthesis is meant for a substitutionDick said:It's not really clear what integral you are actually trying to solve. Is there really a t^2 in the exponent? Is the sinh multiplying that?
it's from the MIT OCW websitedynamicsolo said:I've got a separate question about this: is that upper limit really 'ln 1'? Wouldn't that make the two limits of integration identical? Is someone pulling your leg on this one? Is it a trick question?
rocophysics said:it's from the MIT OCW website
http://ocw.mit.edu/NR/rdonlyres/6055BD0B-FEA6-4BBD-AB05-9E9D81615CAA/0/ocw01exam3.pdf
lol it is both 0, i didn't even notice.
"18.01" is (college) freshman calculus. Every freshman at M.I.T. either "places" in a higher math course or takes 18.01 first semester freshman year (that's my memory from way back). I wouldn't want to be "elitist" but if you look carefully at that test you will see many problems that are easy if you understand the concepts rather than just apply formulas.Gib Z said:Thats an MIT test? I don't believe you. Here I was thinking MIT was an elite University...what grade is test meant to be for?
um yeah, you're definitely a nerd, lol. surprisingly that i did notice that it was "worth" 3 points. but since i didn't notice the lower/upper limits, it didn't click.dynamicsolo said:Bwah-hah-hah! As a classical MIT nerd would declare, "You've been hacked!" (That does explain why that question's only worth 3 points. The lecturer was probably checking to see who was awake...)
Whoa! Good ol' 18.01 -- takes me back...
ProTip: Watch out if someone at MIT has something to do with an exam like this. They love to pull a fast one on the unwary at some point... (It's a place where parties unknown break into a "secure" area and adorn the Great Dome of the main building with something monumental almost every year.* They also measure bridge spans in smoots... What can you expect?)
*In 2003, to mark the centennial of heavier-than-air aviation, a rough reproduction of a Wright Flyer appeared atop the building overnight...
math http://ocw.mit.edu/OcwWeb/Mathematics/index.htm#undergradGib Z said:Thats an MIT test? I don't believe you. Here I was thinking MIT was an elite University...what grade is test meant to be for?
rocophysics said:um yeah, you're definitely a nerd, lol.
The integral and derivative are two mathematical operations that are closely related. The main difference is that the derivative measures the rate of change of a function at a given point, while the integral measures the accumulated value of a function over a given interval.
The right approach is important when using integral and derivative because it ensures that the calculations are accurate and meaningful. Without the right approach, the results may be incorrect and misleading.
To check if the integral and derivative were calculated correctly, you can use the fundamental theorem of calculus. This theorem states that the integral of a function is equal to the original function, and the derivative of the integral is equal to the original function. Therefore, if these conditions are met, then the calculations were done correctly.
Integral and derivative have numerous real-life applications in fields such as physics, engineering, economics, and finance. Some examples include calculating the velocity and acceleration of objects, predicting stock market trends, and optimizing manufacturing processes.
Yes, it is possible to have a negative value for integral and derivative. In mathematics, negative values are simply a representation of direction or magnitude, and they can be interpreted in various ways depending on the context of the problem. For example, a negative integral may represent a decrease in the accumulated value of a function over an interval, while a negative derivative may represent a decrease in the rate of change of a function at a given point.