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Integrals of Exponential Functions quiz

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  • What is the integral of b^x with respect to x?
    The integral of b^x dx is b^x divided by ln(b), plus the constant of integration c.
  • What must the base b satisfy in the integral of b^x dx?
    The base b must be greater than zero and not equal to one.
  • How do you find the integral of e^x dx?
    The integral of e^x dx is e^x plus the constant of integration c.
  • Why does the integral of e^x dx simplify to e^x?
    Because ln(e) equals 1, so e^x/ln(e) simplifies to e^x.
  • What is the integral of 7^x dx?
    The integral is 7^x divided by ln(7), plus c.
  • How do you apply the constant multiple rule when integrating 3*(1/2)^x dx?
    Pull the constant 3 out front and integrate (1/2)^x dx separately.
  • What is the integral of (1/2)^x dx?
    It is (1/2)^x divided by ln(1/2), plus c.
  • How can you simplify ln(1/2) using log properties?
    ln(1/2) can be rewritten as ln(2^-1), which is -ln(2).
  • What is the simplified form of 3*(1/2)^x/ln(1/2)?
    It is -3/(2^x * ln(2)).
  • What is the integral of 8^x dx?
    The integral is 8^x divided by ln(8), plus c.
  • How do you integrate a sum like 3*(1/2)^x + 8^x dx?
    Split the integral into two parts and integrate each term separately.
  • What is the integral of 5*e^x dx?
    It is 5*e^x plus the constant of integration c.
  • How do you integrate 3x^4 - πe^x + 2 dx?
    Break it into three integrals: 3x^4 dx, -πe^x dx, and 2 dx, then integrate each term.
  • What is the integral of 3x^4 dx?
    It is (3/5)x^5 plus c.
  • What is the integral of πe^x dx?
    It is πe^x plus c, since π is a constant.