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Multivariable Calculus

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Difficult

Convert Double Integral to Single Integral

MVCALC-KBRFXG

Let $f$ be a continuous function on the unit disk, convert the double integral:

$$I=\iint_{x^2+y^2\leq 1} f(3x+4y)dxdy$$

...to a single integral using appropriate change of variables.

A

$\int_0^1 f(5u)du$

B

$5\int_{-1}^1 f(u)du$

C

$2\int_{-1}^1 \sqrt{1-u^2} f(5u)du$

D

$\int_0^1 \sqrt{1-u^2} f(5u)du$

E

$\int_{-1}^1 uf(u)du$