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Question
Using integration, find the area of the region bounded by the line 2y = 5x + 7, x- axis and the lines x = 2 and x = 8.
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Solution
Given that: 2y = 5x + 7, x-axis, x = 2 and x = 8.
Let us draw the graph of 2y = 5x + 7
⇒ y = `(5x + 7)/2`
| x | 1 | –1 |
| y | 6 | 1 |
Area of the required shaded region
= `int_2^8 ((5x + 7)/2) "d"x`
= `1/2[5/2 x^2 + 7x]_2^8`
= `1/2[5/2 (64 - 4) + 7(8 - 2)]`
= `1/2[5/2 xx 60 + 7 xx 6]`
= `1/2[150 + 42]`
= `1/2 xx 192`
= 96 sq.units
Hence, the required area = 96 sq.units
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