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Multivariable Calculus

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Change of Variable

MVCALC-XYERXU

When we perform a variable change using $y=2x$ in the integral:

$$I=\int_0^2 (x+1)dx$$

...we end up obtaining the integral:

$$I=\int_0^4 (\frac{y}{2}+1)f(y)dy$$

Find $f(y)$.

A

$\cfrac{1}{2}$

B

$2y+1$

C

$y+1$

D

$2$

E

None of the above