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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
  • Can the Volume of a Sphere be Calculated by . . . - Physics Forums
    The the area integral is a double integral over r and the azimuthal angle The volume integral is over r, the azimuthal angle and the polar angle You're missing some parts of the "big picture" about spherical coordinates You kind of skipped the intergrating over the azimuthal angle part by including 2 \pi straight into your integrand
  • 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 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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