The Missing Integral 1

  • Drag the slider and check that for every n, x^n has a derivative
  • Switch on the Integral and check for the INTEGRAL of x^n. One is missing, which one? Try to Integrate by hand using the Integration rule you know for x^n. Explain why it doesn’t work.
  • Integration is used to find the area under the curve of a function. So if we would find an Interval for which the area under the curve is 1, Then the x and y-values of that interval would give a hint as to the function we are looking for (the integral). The area under the curve (by definition) is given to be F(b) - F(a). Let’s choose a to have the value of 1 hence the area is F(b)-F(1)
  • Try and make the area under the curve equal to one.  Then solve the riddle: F(1) = … and F(b) = …. Which function makes that happen?