MULTIPLE INTEGRAL

Change of Order

7 Topics
VECTOR CALCULUS

Divergence and Curl

4 Topics
Line Integral

4 Topics
Greens Theorem

6 Topics
Surface Integral

6 Topics
Gauss Divergence Theorem

8 Topics
Stokes Theorem

5 Topics
Conservative Vector Field

3 Topics
DIFFERENTIAL EQUATIONS

Orthogonal Trajectory

2 Topics
MATRICES

Introduction to Matrices

7 Topics
Linear Equations

6 Topics
Determinant

7 Topics
Revision of Matrices

6 Topics
Similar Matrices

1 Topic
DIFFERENTIAL CALCULUS

Monotonicity

5 Topics
Critical Points

3 Topics
Maxima and Minima

3 Topics
Lagrange Mean Value Theorem

5 Topics
Function of Two Variables

7 Topics
Fourier Series

1 Topic
**Example 1 :**

If determine the value of where *C* is the curve in the *xy* plane from (0, 0) to (1, 2).

**Solution :**

The curve lies in *xy* plane, so,* z* = 0. *z* can never be taken as independent variable *z* is a dependent variable. Now, out of *x* and *y*, any one variable can be taken as independent.

Suppose *x* is taken as independent variable

So, the line integral reduces to a definite integral.

If *y* is taken as independent variable then* x* can be expressed in terms of *y* as

So,

So, the line integral reduces to a definite integral

**Example : 1 **

Evaluate around a circle

**Solution :**

Let *C* denotes the circle. The parametric equations of circle is

Here, *x* and *y* have been expressed in terms of parameter which varies from 0 to as one traverses the circle.

So,

Here, *r* is a constant, because integral is carried over a circle.

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