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The discussion highlights the need to apply the cosine. Now multiply the integrands together double integrate over x and y. Coz sometimes when i approach questions like that i just don't know how to.
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Does that work out to your. If you do this and get the original integrand, your work is correct. \\int \\frac{dx}{(x^2+y^2)^\\frac{3}{2}} now, i know there are quite a few straightforward answers to this.
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Dx i bet its really simple but i have looked in several books and they just give the answer.
Similarly, since you know that the derivative of arctan is 1/ (1+x^2), you know that the integral of the latter is the former. Note that , so the absolute value isn't needed. Well, so i really want to integrate what's shown in the title: Is there any way to find an explicit formula for this integral?
And have you tried their suggestion for i and iii? $$\int \frac {1} {x^2 + 2} dx$$ my attempt is $$\ln |x^2 + 2| + c$$ at least this time you showed an attempt. Making substitution for x^2 still leaves a factor x in the denominator since u = x^2 implies du = 2 x dx. What happened to the exponential after you integrated by parts?
The result then would give a square root of u in the integral, which i cannot solve by integration by parts.
But what i really want is how people who do math got this formula in the first place. The integral of sin² (x) from 0 to 2π is π, which corresponds to half the period when considering the relationship between angular frequency and period (ω = 2π/t). Is there a chain rule for integral? You can move the d/da inside the integral (justifying this is a little tricky, but i'm sure you don't need to worry about that).
When you integrate cos (x), you don't have to substitute anything, because you know that the derivative of sin (x) is cos (x), so the integral of cos (x) is sin (x). Integrating sin² (ωt) over one period results in t/2 due to the properties of the sine function and its average value over a complete cycle. I don't just want a formula that. How to do integral for cos (x^2)dx?
Could someone please help me with the integral of 2^x.
You can always check your work with an indefinite integral by differentiating your answer. Homework statement try ∫∫g x^2 da ;value is the region bounded by the ellipse 9x^2+4y^2=36 homework equations the attempt at a solution i think i have to change the variables to polar coordinate or u,v function but i have no idea.
