Question

Consider a continuous function f such that F'(x) = f(x) for all real values of x. Find the integral evaluated from 2 to 7 of f(5x)dx. Any calc people get this?

Answer 1

clearly you are not expected to find a number, right?

Answer 2

change the variable \(u=5x\)

Answer 3

and \(du=5dx\) so \(\frac{1}{5}du=dx\) also change the limits of integration \(u(2)=5\times 2=10\) and \(u(7)=35\) then rewrite the integral as
\[\frac{1}{5}\int_{10}^{35}f(u)du\]

Answer 4

Umm so my answers are
A) 5F(7) - 5F(2)
B) (1/5)F(7) - (1/5)F(2)
C) 5F(35)- F(10)
E) (1/5)F(35) - (1/5)F(10)

Answer 5

D) F(35) - F(10)