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- 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
- Solving Integrals for e^-ax^2: (i), (ii) (iii) - Physics Forums
Solving Integrals for e^-ax^2: (i), (ii) (iii) sanitykey Nov 9, 2006 Integrating
- 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 Some participants clarify that the method of
- How Do You Integrate (dx dt) dx in Physics Problems?
Good Night, Can someone please tell me how to do: ∫ b (dx dt) ⋅ dx ? Like in the work done by a force which is proportional to the velocity (like drag) I tried to change dx to v dt but couldn´t go much further Thank you in advance
- Can the Volume of a Sphere be Calculated by . . . - Physics Forums
i noticed that if i integrate 2 \\pi r i get \\int 2 \\pi r dr=\\pi r^2 i figured its because the area of a circle can be seen as the sum of circumference's of circles with radius 0 to radius r i was thinking if the half volume of a ball also be seen as made from the sum of areas of circules
- How can I integrate e^ {ax^ {2}+bx+c} without getting tangled?
The Attempt at a Solution I tried to substitute ax^ {2}+bx+c by -y^ {2} but I get hopelessly tangled (PS : how do get the tex tags to not create an equation environment but stay inline?) Use itex itex for inline LATEX Use \displaystyle with that to keep ∫ , fractions, etc full size See above Try completing the square for ax^ {2}+bx+c
- Integrate exp(-x^2), dx - Physics Forums
This integral can be done the same way that the integral of exp (-x 2) can be done First, write the integral of x 2 exp (-x 2) from zero to infinity Then write the integral of y 2 exp (-y 2) from zero to infinity (they're both exactly the same as your integral) Now multiply the integrands together double integrate over x and y
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