Question
Using integration find the area of the triangular region whose sides have equations y = 2x + 1, y = 3x + 1 and x = 4.
✓
Answer
Getting the points of intersection as
A(0,1),B(4, 9) and C(4,13)
Area $\Delta$ ABC = $\int\limits_0^4\text{x}\text{(3x + 1)}\text{dx}-\int\limits_0^4\text{(2x + 1)}\text{dx}$
$=\int\limits_0^4\text{x dx}=\Bigg[\frac{\text{x}^{2}}{\text{2}}\Bigg]^4_0=8\text{sq. units}$.
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