Question

The value of \(\iint_R y^2x\,dy\,dx\) over the rectangle \(R=\{(x,y):-3\le x\le 2,\;0\le y\le 1\}\) is given by:

• A. $-\frac{1}{6}$
• B. $-\frac{1}{2}$
• C. $-\frac{5}{6}$
• D. $\frac{5}{6}$

Hint:

Whenever the limits of a double integral are constant and the integrand is of the form $f(x) \cdot g(y)$, always separate them into the product of two single integrals to save calculation steps.

Answer 1

The Correct Option is C