Question

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 1

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