VTU Engineering Maths 1 change into Polar coordinates interesting example(PART-10)
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7 سال پیش
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In this video explaining change
In this video explaining change into polar coordinates. This method is very easy and simple. This integration is doable integration.
Here are the steps involved in changing an integral from Cartesian to polar coordinates:
Determine the region of integration: You will need to identify the limits of integration in terms of r and θ.
Express x and y in terms of r and θ: This involves using the equations x = r cos θ and y = r sin θ to convert the integrand from Cartesian coordinates to polar coordinates.
Calculate the Jacobian: This is the determinant of the transformation matrix that converts from Cartesian to polar coordinates. In two dimensions the Jacobian is simply r.
Rewrite the integral in terms of r and θ: This involves replacing x and y with their polar coordinate equivalents and replacing dxdy with r dr dθ.
Evaluate the new integral: This involves integrating the integrand using the new limits of integration.
Check your work: Make sure that the result of the new integral is consistent with the original integral.
#changeintoPolar #integration
18MAT11 Module1: Differential Calculus1
Differential Calculus1: 22MAT11
18MAT11 Module2: differential Calculus2
Series Expansion & Multivariable Calc...
18MAT11 Module3: Integral CalculusMultiple Integrals & Beta and Gamma f...
18MAT11 Module4: Ordinary differential equations
Ordinary differential equations (ODE'...
Linear Algebra: 18MAT11 MODULE 5
Linear Algebra: 22MAT11
18MAT21 MODULE 1:Vector Calculus
Vector Calculus
18MAT21 MODULE 2:Differential Equation higher order
Ordinary Differential Equation of Hig...
18MAT21 MODULE 3: Partial differential equations
Partial differential equations
18MAT21 MODULE 4: Infiinite series & Power series solution
Special Functions
18MAT21 MODULE 5: Numerical methods
Numerical methods
18MATDIP41 Linear Algebra
18MATDIP41 Linear Algebra
18MATDIP41 Numerical Methods
18MATDIP41 Numerical Methods
LAPLACE TRANSFORM : 18MAT31
LAPLACE TRANSFORM
Fourier Transforms,Z-transform : 18MAT31 & 17MAT31
Fourier Transforms,Z-transform: 21MAT...
Joint Probability & Sampling Theory: 18MAT41 & 17MAT41
Joint Probability & Sampling Theory
Probability Distributions: 18MAT41 & 17MAT41
Probability Distributions
Calculus of Complex Functions: 18MAT41 & 17MAT41
Complex Analysis & Complex Integrations
Curve fitting & Statistical Method 18MAT41 17MAT31
Statistical Method & Curve fitting
COMPLEX NUMBER: 18MATDIP31
COMPLEX NUMBER: 18MATDIP31
Vector differentiation 18MATDIP31 & 17MATDIP31
Vector differentiation 18MATDIP31,17M...
Differential Calculus & Partial Differential 18MATDIP31 & 17MATDIP31
Differential Calculus & Partial Diffe...
Here are the steps involved in changing an integral from Cartesian to polar coordinates:
Determine the region of integration: You will need to identify the limits of integration in terms of r and θ.
Express x and y in terms of r and θ: This involves using the equations x = r cos θ and y = r sin θ to convert the integrand from Cartesian coordinates to polar coordinates.
Calculate the Jacobian: This is the determinant of the transformation matrix that converts from Cartesian to polar coordinates. In two dimensions the Jacobian is simply r.
Rewrite the integral in terms of r and θ: This involves replacing x and y with their polar coordinate equivalents and replacing dxdy with r dr dθ.
Evaluate the new integral: This involves integrating the integrand using the new limits of integration.
Check your work: Make sure that the result of the new integral is consistent with the original integral.
#changeintoPolar #integration
18MAT11 Module1: Differential Calculus1
Differential Calculus1: 22MAT11
18MAT11 Module2: differential Calculus2
Series Expansion & Multivariable Calc...
18MAT11 Module3: Integral CalculusMultiple Integrals & Beta and Gamma f...
18MAT11 Module4: Ordinary differential equations
Ordinary differential equations (ODE'...
Linear Algebra: 18MAT11 MODULE 5
Linear Algebra: 22MAT11
18MAT21 MODULE 1:Vector Calculus
Vector Calculus
18MAT21 MODULE 2:Differential Equation higher order
Ordinary Differential Equation of Hig...
18MAT21 MODULE 3: Partial differential equations
Partial differential equations
18MAT21 MODULE 4: Infiinite series & Power series solution
Special Functions
18MAT21 MODULE 5: Numerical methods
Numerical methods
18MATDIP41 Linear Algebra
18MATDIP41 Linear Algebra
18MATDIP41 Numerical Methods
18MATDIP41 Numerical Methods
LAPLACE TRANSFORM : 18MAT31
LAPLACE TRANSFORM
Fourier Transforms,Z-transform : 18MAT31 & 17MAT31
Fourier Transforms,Z-transform: 21MAT...
Joint Probability & Sampling Theory: 18MAT41 & 17MAT41
Joint Probability & Sampling Theory
Probability Distributions: 18MAT41 & 17MAT41
Probability Distributions
Calculus of Complex Functions: 18MAT41 & 17MAT41
Complex Analysis & Complex Integrations
Curve fitting & Statistical Method 18MAT41 17MAT31
Statistical Method & Curve fitting
COMPLEX NUMBER: 18MATDIP31
COMPLEX NUMBER: 18MATDIP31
Vector differentiation 18MATDIP31 & 17MATDIP31
Vector differentiation 18MATDIP31,17M...
Differential Calculus & Partial Differential 18MATDIP31 & 17MATDIP31
Differential Calculus & Partial Diffe...
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