If f is continuous and integral 0 to 4 f(x)dx=10, find integral 0 to 2

Cabiolab 2021-10-07 Answered
If f is continuous and integral 0 to 4 f(x)dx=10, find integral 0 to 2 f(2x)dx
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Expert Answer

StrycharzT
Answered 2021-10-08 Author has 102 answers
We will start working with the integral 02f(2x)dx
Substitute 2x=u and 2dx=du
=1202f(2x)(2dx)
Limits of integration will change from 02 to 2×02×2=04
1204f(u)du
Remember that abf(u)du=abf(x)dx
=1204f(x)dx
It is given that
04f(x)dx=10
=12×10=5
Result: 02f(2x)dx=5
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