
How do you integrate two variables?
Answer
162.6k+ views
Hint: A two-dimensional region can be integrated using double integrals. They enable us to, among other things, calculate the volume beneath a surface.
Complete step by step Solution:
Two variables are multiplied together in the integration of two variables, sometimes referred to as integration by parts.
Assuming two \[p\] and \[q\] functions of the variable \[x\] and both the algebraic function.
Then we use the formula \[\int {pqdx} = p\int {qdx} - \int {\dfrac{{dp}}{{dx}}\left( {\int {qdx} } \right)} + c \] to find the integration value.
In this formula we can take \[p\] as the first function and \[q\] as the second function.
As both the functions are functions of \[x\] then we can choose any one of the functions as the first function and the other function as the second function.
If we have both the functions are different functions like exponential, algebraic, trigonometric etc.
Then we choose the first and second functions with the ILATE rule.
ILATE rule is used for finding the first and second functions for this formula.
The full form of ILATE is inverse, logarithm, algebraic, trigonometric, and exponent.
After successfully choosing the first and second functions of \[x\] we solve the expression to get the final expression.
Note: Students get confused when in a given expression they have both the functions are the same form, like both are exponential, or both are trigonometric then they have a doubt which chooses the first and second function. We can take any one of them as the first function and the other function as the second function.
Complete step by step Solution:
Two variables are multiplied together in the integration of two variables, sometimes referred to as integration by parts.
Assuming two \[p\] and \[q\] functions of the variable \[x\] and both the algebraic function.
Then we use the formula \[\int {pqdx} = p\int {qdx} - \int {\dfrac{{dp}}{{dx}}\left( {\int {qdx} } \right)} + c \] to find the integration value.
In this formula we can take \[p\] as the first function and \[q\] as the second function.
As both the functions are functions of \[x\] then we can choose any one of the functions as the first function and the other function as the second function.
If we have both the functions are different functions like exponential, algebraic, trigonometric etc.
Then we choose the first and second functions with the ILATE rule.
ILATE rule is used for finding the first and second functions for this formula.
The full form of ILATE is inverse, logarithm, algebraic, trigonometric, and exponent.
After successfully choosing the first and second functions of \[x\] we solve the expression to get the final expression.
Note: Students get confused when in a given expression they have both the functions are the same form, like both are exponential, or both are trigonometric then they have a doubt which chooses the first and second function. We can take any one of them as the first function and the other function as the second function.
Recently Updated Pages
Fluid Pressure - Important Concepts and Tips for JEE

JEE Main 2023 (February 1st Shift 2) Physics Question Paper with Answer Key

Impulse Momentum Theorem Important Concepts and Tips for JEE

Graphical Methods of Vector Addition - Important Concepts for JEE

JEE Main 2022 (July 29th Shift 1) Chemistry Question Paper with Answer Key

JEE Main 2023 (February 1st Shift 1) Physics Question Paper with Answer Key

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Degree of Dissociation and Its Formula With Solved Example for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

JoSAA JEE Main & Advanced 2025 Counselling: Registration Dates, Documents, Fees, Seat Allotment & Cut‑offs

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

NCERT Solutions for Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations

NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations

NCERT Solutions for Class 11 Maths In Hindi Chapter 1 Sets

NEET 2025 – Every New Update You Need to Know
