Hi
We know that and we want to calculate
Let u = 2x
Then x going from 0 to 2, u is going from 2x0=0 to 2x2=4
and du = 2dx or dx = du/2
Therefore
Question:
"If f is continuous and if this (integral (f(x)dx) from 0 to 4 - Wolfram|Alpha) integral = 10. Then find, this(integral (f(2x)dx) from 0 to 2 - Wolfram|Alpha) integral.
I have no idea how to do this. Someone please help me!
Answer:
5
Any input would be greatly appreciated!
Thanks in advance!
If you are asking why
, that's true because the variable inside the integral is a "dummy variable". is number, not a function of x. Similarly is a number not a function of u. Since it doesn't matter what we call the variable, the two numbers must be equal.
The same thing happens with sums:
so .