If f is continuous find the following

Question

If f is continuous and ∫(Top: 24, Bottom:0) f(x)dx=50, find ∫(Top:4, Bottom:0) f(6x)dx)

I'm not very good with my substitution, and I have been having some trouble with this. If you can help, thank you!.

Answer 1

Mathematically, u = 6x, so du = 6 dx, and dx = 1/6 du, and we have 1/6 the original integral, (once you have rewritten in terms of u, just swap x for u)

Conceptually, you have changed the horizontal scale by a multiple of 1/6 and not changed the vertical scale, so the area is 1/6 what it was.

Thus, the area is 1/6 * 50 = 50/6 of 25/3 or 8 1/3