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The indefinite integral is the anti-derivative - so the question is, "What function has this given function as a derivative". And if you add a constant to a function, the derivative of the function doesn't change. Thus, for example, if the derivative is y' = 2x, the original function might be y = x squared. However, any function of the form y = x squared + c (for any constant c) also has the SAME derivative (2x in this case). Therefore, to completely specify all possible solutions, this constant should be added.
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What is the value of the rate constant?
I depends on the problem. The rate constant is different depending on the problem in which it occurs.
Is there a constant in the problem of 46n?
the coefficient is 46 and the constant is 0
How do you find the derivative for f(x) integral (1-t2)(1 plus t4) from sin2x to 1?
My suggestion is to multiply the binomials and do the integration directly, and then differentiate the result with respect to x. (If that doesn't work, feel free to send me a picture of the problem and I'll give it another try.)
What is the difference between vertical and horizontal integration?
Horizontal integration is the process of merging similar industries, industries that produce similar products. Vertical integration is the process of buying out suppliers of that particular industry. The main difference is that horizontal integration buys the competing companies while vertical integration aims at the raw material sources necessary to produce that product
What is the indefinite integral of 2x ln2x dx?
In order to work out this problem, we need to learn how to apply the integration method correctly.The given expression is ∫ 2xln(2x) dx.Instead of working out with 2x's, we let u = 2x. Then, du = 2 dx or du/2 = dx. This method is both valid and easy to avoid working out with too much expressions. You should get:∫ uln(u) (du/2)= ½ ∫ uln(u) duUse integration by parts, which states that:∫ f(dg) = fg - ∫ g(df)We let:f = ln(u). Then, df = 1/u dudg = u du. Then, g = ∫ u du = ½u²Using these substitutions, we now have:½(½u²ln(u) - ½∫ u du)= ¼(u²ln(u) - ∫ u du)Finally, by integration, we obtain:¼ * (u²ln(u) - ½u²) + c= 1/8 * (2u²ln(u) - u²) + c= 1/8 * (2(2x)²ln(u) - (2x)²) + c= 1/8 * (2x)² * (2ln(u) - 1) + c= ½ * x² * (2ln(2x - 1)) + c
