I this a use for calculus? Bacteria reproduces at x^2. If you integrate the derivitive will the area under the
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Integrating the derivitive leaves you with the initial equation x^2 since an integral is the opposite to a derivitive much like addition is the opposite of subtraction.  If you add 2 then subtract 2 you have the same answer.  As for the area under the curve, this will indeed be your entire population.
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when you integrate 1/x you get In |x|\n\nso the answer is -1/2 * In |x| + constant term\n\n\nYou can use substitution, but there's not much point, because you'll get 1/u then (which is the same thing). 1/x is a well known integrand. You'd be better just memorising that the integral of 1/x = In(x)
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If you were to integrate f(x) from 0 to pi/2\n\nit wold be  int(f,0,pi/2).
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u can even use calculus to find this out
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if f(x) = ∫[t = x to 0] 1/ (1 + t + t²) dt\n\nf'(x) = -1/ (1 + x + x²)\n\nf''(x) = (1 + 2x)/(1 + x + x²)²\n\nFor concave UP f''(x) > 0\n\nSo 1 + 2x > 0 (as (1 + x + x²)² > 0 for all x)\n\nie x < -1/2
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If ∫f(x)dx = y(x), then f(x) = d y(x) / dx;  So to get the answer, take the derivative of the expression x^2 - 2x + 1.  The value of the integral at limit 1 is  a constant and will not appear in the derivative.
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Do you have limits between which to calculate the area? If not you can solve for the values where f(x) = g(x)\nyou should get two values since g(x) is a second degree function.\nThe 2 values are your limits for integration.\nIntegrate each function with respect to dx between the limits and take the difference of the two. Since area is always positive the value should be the absolute value of the difference.\n\nI think that is enough hint. I won't do it for you. But here is what you should start with:\n\nsolve for x where f(x) = g(x), the two values for x are the two limits for your integration, for example x1 and x2.\nthen integrate\n  x1\n| ∫( f(x) - g(x) ) dx |\n  x2
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Depends on what variable you're differentiating with respect to:\ndV/dr : 2/3*pi*r*h\ndV/dh:  1/3*pi*r^2
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dx/dt+ax=b :P\n\n\nmathematica had some online find-the-derivitive program, last I remember
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In the textbook you got the question out of. Read it! LOL
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calculus was largely invented to describe problems in physics;  physics is largely reliant on the framework of calculus for its meaning.\n\ndifferentiating a function and making the constant go away doesn't introduce a "50% error" (whatever that means); it means that constants are just that -- constant -- and do not vary with the independent variable.\n\nyou're right about one thing though:  an erroneous conclusion has certainly occurred here.
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she asked math not included.  You'll need some in depth statistics for genetic engineering and bioinfomatics.  You'll need some amount of differential equation if u want to pursue a career in microbiology and biochem etc etc.  contact me for more info. what exactly is math at 12th grade?  have u taken an actual calculus yet?
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Anytime you have a problem that is continuous, as opposed to discrete, you will need to use either integration or differentiation to characterize the solution.  That means to say that every problem that involves time in one way or another will necessitate the use of calculus to find an answer at some instant in time.  If the problem is such that you can approximate the answer, then you can discretize the parameters as small slices of time and come up with an approximate answer - without using calculus.
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No.\n\nIt means that the slope of the curve y = x^2 at a given point is equal to twice the value of x at that point.\n\nThe change in y for an infinitesimally small change in the value of x is equal to twice the value of x at that point.\n\nYour interpretation, "for every change in x there is a change of 2 [in y]", would correspond to a derivative (or slope) of 2, not of 2*x.  The function, y = 2*x + constant would have a derivative dy/dx = 2.
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This is a Frequently Asked Question. Following is a modified previous answer:\n\n\nIf one has a function f as a map from the real line into itself, one also has the graph of the function as the set of all points (x,f(x)) as a curve in the Cartesian plane. If one wanted to know the area between the x-axis and this curve over some interval on the x-axis, one would use a definite integral. If one wanted to know the slope of a line tangent to the curve at some point (x,f(x)) on the curve, one would use the derivative of the function f at the point x. Both of these operators are very useful in physics, as most physical properties are defined as changes in some property. If p(x) is a graph of some physical property over the domain it is a function of, then the change in p with respect to x approaches the slope of the tangent line to p(x) as one considers smaller and smaller changes in x. Thus, the derivative is the ideal way of talking about continuous changes in physical properties.\n\nFor differentiation in one dimension, you can use the definition: the derivative of a function f at the (domain) point x is the limit as h approaches 0 of the slope of the secant line [f(x+h)-f(x)]/h. Visually, we take a secant line to the curve that passes through the points (x, f(x)) and (x+h, f(x+h)) and rotate it (see what happens as h gets smaller) until it only touches the curve once (it is now tangent to the curve). This line is unique at each point.\nIn more than one dimension, using the definition is cumbersome for anything other than proving when a derivative does or does not exist, so we use a useful theorem that says the derivative of a function f from R (the real line) into R^n (n-dimensional Euclidean space) is just the vector of partial derivatives of f. Ie., if f(x,y) = x^2 + y^2 (the graph is a circular paraboloid), then Df(x,y) = (df/dx, df/dy) = (2x, 2y). Partial derivatives are taken relative to one variable only; they end up treating the other variables as constants. The technical definition of the partial of f with respect to x at the point x0 is what you suspect it would be: the limit as h approaches zero of the slope of the secant line [f(x0+h, y) - f(x0,y)]/h.\nOnce one gets to these derivatives of multivariable functions though, one must be very careful, as the existence of all partial derivatives at a point does not mean the derivative exists at that point.\nOnce one gets a bit of experience taking derivatives using the definition, one can derive some simple derivative rules which allow you to take derivatives of elementary functions without explicitly doing all that limit mumbo-jumbo. A list of common differentiation rules can be found here: http://mathworld.wolfram.com/Derivative.html .\n\nIntegration is a more delicate matter. If you're doing a definite Riemann integral (finding the area under a curve), it is the limit of a Riemann sum as you increase the number of rectangles under the curve ( See http://mathworld.wolfram.com/RiemannSum.html ). The indefinite integral is just the function that will return the definite integral when you take the difference between two points.\nSometimes the rectangles will not converge to any finite value or it does not have a unique convergence and we say the function is not integrable on that interval (Take f(x) = 1/x on the interval [0,1] for example). A more technical definition of integration will help integrate more pathological functions, but you can look up this definition yourself in a real analysis text; it's not that different from summing rectangles.\nAgain, with integrals we have a very nice theorem that tells us that the indefinite integral of the derivative of a function f is f itself. This is the fundamental theorem of calculus, and it takes a lot of work out of finding an integral. For example, if f(x) = 2x, we know from our experience with taking derivatives that the indefinite integral of f(x) is just F(x) = x^2 + C where C is an unknown constant since the deriv
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Calculus is a pure mathematical theory. It has 2 main applications 1 to enable calculation of the gradiant of a curve at any point on the curve, this gives you rate of change of x with respect to y. e.g. if y axis was metres and x axis was seconds this would give you the rate of change of distance with respect to time in m/s i.e. speed.\n\nIf you want to understand differentiation, I suggest you google differentiton from first principles.\n\nThis is one of the physical applications of differentiation.\n\nThe other application is to take a curve and calculate the area underneath it between two points on the curve. Say you have a curve where the y axis is speed in m/s and the x axis is time in seconds. Then the area under the curve would give you the distance travelled between points x=m and x=n. So if you integrate a velocity vs time formula you get distance travelled. This is an application of integration. To understand integration google "simpsons rule".\n\nThere are many more applications of this in physics relating to rate of change & intergration \n\ne.g Electical current is the rate of change of voltage with respect to resistance. dv/dr\n\ne.g. Power in an electical circuit is the integral of current (I) w.r.t to resistance dr
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Yes since ∫f(x) dx = ∫x dx\n= ½x² + c where c is ANY constant.