Write the Integral with the Order of Integration Reversed (Changing $$\int _ { - 1 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 + y } } f ( x , y ) \mathrm { d } x \mathrm {~d} y$$

question 105

Multiple Choice

Write the integral with the order of integration reversed (changing the limits of integration as necessary) . $$\int _ { - 1 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 + y } } f ( x , y ) \mathrm { d } x \mathrm {~d} y$$

• A) \(\int _ { 0 } ^ { \sqrt { 2 } } \int _ { \sqrt { x } - 1 } ^ { 1 } f ( x , y ) \mathrm { d } y \mathrm {~d} x\)
• B) \(\int _ { 0 } ^ { \sqrt { 2 } } \int _ { x ^ { 2 } - 1 } ^ { 1 } f ( x , y ) \mathrm { d } y \mathrm {~d} x\)
• C) \(\int _ { 0 } ^ { 1 } \int _ { 1 } ^ { x ^ { 2 } - 1 } f ( x , y ) \mathrm { d } y \mathrm {~d} x\)
• D) \(\int _ { - 1 } ^ { 0 } \int _ { x ^ { 2 } - 1 } ^ { 1 } f ( x , y ) \mathrm { d } y \mathrm {~d} x\)
• E) \(\int _ { 0 } ^ { \sqrt { 2 } } \int _ { \sqrt { x - 1 } } ^ { 1 } f ( x , y ) \mathrm { d } y \mathrm {~d} x\)

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Definitions:

Recombinant DNA

Composite DNA made in a laboratory by joining DNA fragments from multiple sources.

Restriction Enzymes

Enzymes that cut DNA at specific sequences, widely used in molecular biology for cloning and DNA manipulation.

Ligases

Enzymes that catalyze the joining of two molecules by forming a new chemical bond, often requiring the expenditure of energy derived from ATP.

Polymerase

An enzyme that synthesizes long chains or polymers of nucleic acids.