Question

For the function:
a) integrate by hand to find the area under the curve btwn the given x-values
b) verify your answer to part (a) by having your calc graph the function and find the area (using command like Fnlnt or Sf(x)dx

f(x) = 1/x^3 from x=1 to x=4

Answer 1

what's the trouble? It's just a straightforward integration.
1/x^3 = x^-3, so
∫[1,4] x^-3 dx = -1/2 x^-2 [1,4] = (-1/2 * 4^-2)-(-1/2 * 1^-2) = -1/32 + 1/2 = 15/32