Hey guys n gals
somehow forgot, but when solving a definite integral say functiong y=x^2 from 0 to 10... how come when you do the integral it doesnt include anything below y=0.... i know why but i just neeed the proof
and when doing area problems under a curve for example sinx {0, 2pi} the value is 0 but the net area is ???
Proof of what? That the square of a real number is never negative? Essentially it is that the product of two positive numbers is positive and that the product of two negative numbers is positive: if you are squaring a number, you are multiplying it by itself so you are always multiplying numbers of the same sign.Originally Posted by mpl06c
The "area under the curve" normally means the area below the graph and above the x-axis. For x between pi and 2pi, there is no such are because y= sin(x) is below y= 0. I suspect you mean the area bounded by y= sin(x) and y= 0. Because "area" is never negative, you are subtracting "higher value" minus "lower value". From 0 to pi, the higher value is sin(x) but from pi to 2pi, the higher value is 0 so you have to do that as two separate integrals:and when doing area problems under a curve for example sinx {0, 2pi} the value is 0 but the net area is ???- 0)dx+ \int_\pi^{2\pi} (0- sin(x)dx)
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