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Chapter: 12th Maths : UNIT 9 : Applications of Integration

Limit Formula to Evaluate Definite Integral as the Limit of a Sum

Definite Integral as the Limit of a Sum | Applications of Integration | Mathematics

Limit Formula to Evaluate ba f ( x)dx

Divide the interval [a , b] into n equal subintervals [ x0, x1 ], [ x1, x2 ], . . . , [ xn-2, xn-1 ], [ xn-1, xn ], such that a = x0 < x1 < x2 < . . . < xn 1 < xn = b . Then, we have x1x0 = x2x1 = . . . = xnxn-1 = b-a / n . Put h = ba / n. Then, we get xi = a + ih, i = 1, 2, , n.

So, by the definition of definite integral, we get





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12th Maths : UNIT 9 : Applications of Integration : Limit Formula to Evaluate Definite Integral as the Limit of a Sum | Applications of Integration | Mathematics

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12th Maths : UNIT 9 : Applications of Integration


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