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junior college 2 | H2 Maths
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definite integrals
Pls help thank you!!
Date Posted: 5 years ago
Views: 271
If x axis is divided into n parts,
height of smallest rectangle = (1/n)²
= 1²/n²
height of next smallest rectangle
= (2/n)²
= 2²/n²
height of largest rectangle
= ((n-1)/n)²
= (n-1)²/n²
Area , A = area of all rectangles
= area of smallest rectangle + .. ... + area of largest rectangle
= (1²/n²)(1/n) + (2²/n²)(1/n) + ... ...
+ ((n-1)²/n²)(1/n)
= 1/n³ (1²) + 1/n³ (2²) + ... + 1/n³ (n-1)²
Notice you can factor out the 1/n³ and the addition becomes a summation of r² , with first term r = 1 and last term is the (n -1)th term.
height of smallest rectangle = (1/n)²
= 1²/n²
height of next smallest rectangle
= (2/n)²
= 2²/n²
height of largest rectangle
= ((n-1)/n)²
= (n-1)²/n²
Area , A = area of all rectangles
= area of smallest rectangle + .. ... + area of largest rectangle
= (1²/n²)(1/n) + (2²/n²)(1/n) + ... ...
+ ((n-1)²/n²)(1/n)
= 1/n³ (1²) + 1/n³ (2²) + ... + 1/n³ (n-1)²
Notice you can factor out the 1/n³ and the addition becomes a summation of r² , with first term r = 1 and last term is the (n -1)th term.
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Date Posted:
5 years ago
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