If f is a continuous function such that the integral from 1 to 4 of f of x, dx equals 10, evaluate the integral from 2 to 8 of 2 times f of 2 times x, dx.

Answer: 10

Step-by-step explanation:

Since integral from 1 to 4 of f (x) = 10

To evaluate integral from 2 to 8 of 2 times f (2x), using substitution method

Let U = 2x, dU = 2dx, dx = dU/2

Evaluate the limit, upper limit gives dU = 2*4 = 8, lower limit gives dU = 2*1 = 2.

Since this limit are the same as the limit for the question,

Therefore, F (4) - F (1) = F (8) - F (2) = 10

Substituting dx=dU/2

Gives,

Integral from 2 to 8 of 2 times f (2x) = (1/2) (2) (F (8) - F (2)) = 10