- What is the Integral of 2^(x)? - Physics Forums
The integral of 2^x can be solved using the relationship between derivatives and integrals The derivative of 2^x is ln(2) * 2^x, which leads to the conclusion that the anti-derivative is (1 ln(2)) * 2^x
- What is the Integral of -e^(-x)? • Physics Forums
The integral of -e^(-x) is derived using u-substitution, where u = -x, leading to the result -e^(-x) + C The negative sign arises because the derivative of -x is -1, thus requiring division by -1 during integration The discussion emphasizes that integration can be viewed as the reverse of differentiation, which simplifies the process
- Integral of trig functions over a period • Physics Forums
Can somebody please explain to me why the integral of, for instance, cos ( (2*pi*x) a)*cos ( (4*pi*x) a) vanishes over the interval 0 to a? As I understand it
- Integrate exp(-x^2), dx • Physics Forums
0 integrate exp(-(x C)^k), dx with k>0 and C>0 Hello to you all, i've tried hard to solve this problem related with the wind resources, but so far like Tom Mattsonsaid in is post, i solved the problem to k=2, but i can't solve it to any k>0! integrate exp(-(x C)^k), dx with k>0 and C>0 Is there anyone willing to help me ? Perinhas
- Solving Integrals for e^-ax^2: (i), (ii) (iii) - Physics Forums
Hi, i have a problem which is confusing me :confused: Question: Given that \int_ {0}^ {\infty}e^ {-ax^2} dx = \frac {\sqrt {\pi}} {2\sqrt {a}} What
- Understanding the integral of 1 (1+x^2) • Physics Forums
The integral of 1 (1+x^2) is indeed arctan(x), and no substitution is necessary to find this antiderivative since the derivative of arctan(x) is 1 (1+x^2) Substituting x with tan(Θ) transforms the integrand but can complicate the process unnecessarily, as the antiderivative is already known Understanding the substitution method is valuable, but it is essential to recognize that the goal is
- Integral of 1 (x^2 + 2) dx - 2) dx ? • Physics Forums
Mentor note: Moved from technical section, so missing the homework template How do you integrate this? $$\int \frac {1} {x^2 + 2} dx$$ My attempt is $$\ln
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