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 x3 is 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.
1. x2 and the line y = 2.
1. ∫(3x – 1)(x + 2) dx
2. ∫5cos4x (dx)
Reading Assignment :Solve the evaluation questions given above
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 = x2 , 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
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.Pass WAEC, JAMB, POST-UTME & more in One Sitting for FREE!💃