INTEGRATION [INDEFINITE INTEGRALDEFINITE INTEGRAL AND AREA UNDER CURVE]

The process of reversing differentiation is called Integration. If dy/dx = 3x2, then y could be x3, as the derivative of x3is 3x2.

We say that xis an integral of 3x2 with respect to x. The symbol for integration sign is given by ∫  . The expression to be integrated is put between the  ∫ sign and dx.

∫  3×2 dx could be x3

Since differentiating any constant gives zero, the following also have derivation 3x2.

X3 + 2,  x3 + 4.5,  x3 – 17etc

In general, any function of the form x3 + c, where c is the constant has derivative of 3x2

Hence, ∫  3x2 dx = x3 + C. C is called constant of integration. Because we do not know the actual or definite value of C, this is called INDEFINITE INTEGRAL.

Evaluation

1. x2 and the line y = 2.

 

General Evaluation:

1.                   ∫(3x – 1)(x + 2) dx

2.                   ∫5cos4x (dx)

3.

Reading Assignment :Solve the evaluation questions given above

 

Weekend Assignment:

1.             Evaluate  A. 2/3 B. -2/3 C. -6 2/3 D. 6 2/3

2.             Evaluate   A. 4 B. 2 C. 4/3 D. 1/3

3.             Evaluate   A. – ½ B. 1 C. -1 D. 0

4.                   Find the area enclosed by by the curve y = x, X = 0 and X = 3 A. 9 B. 7 C. 5/2 D. 5

5.                   Given  y = 3x -2, x=3, x=4. Find the area under the curve A. 4/3 B. 17/2 C. 6 D. 3

Theory

1.                   Find the area enclosed between the curve y =x2 + x -2 and the x axis

2.                   Find the area enclosed by the curve y = x2 – 3x + 3 and the y = 1.

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