Question

Which of the following statements are correct:
A. Area of a non negative continuous function from $x = a$ to $x = b$ is $\int_a^b f(x) dx$.
B. $\iint_D f(x,y) dx dy = 0$, where $f(x,y) \ge 0 \, \forall (x,y)$ in $D$.
C. $\iint_R f(x,y) dx dy = \iint_{R_1} f(x,y) dx dy + \iint_{R_2} f(x,y) dx dy$, where $R$ is divided into $R_1$ and $R_2$, and $f$ is integrable on $R_1$ and $R_2$. D. If $f(x,y) = k \, \forall (x,y)$ in $R$, then $\iint_R f(x,y) dx dy = k \times (\text{area of } R)$.
E. $\iint_R C f(x,y) dx dy = C \iint_R f(x,y) dx dy$; $C$ is a constant
Choose the correct answer from the options given below:

• A. A, B Only
• B. A, C, D, E Only
• C. A, C, D Only
• D. C, E Only

Hint:

Double integrals preserve basic properties of single integrals: linearity, domain additivity, and scaling by constants.

Answer 1

The Correct Option is B