Area Under the Curve
Area Between Two Curves
nta_pyq_2024_apr
Grade 12
Question:
One of the points of intersection of the curves $y=1+3x-2x^2$ and $y=\dfrac{1}{x}$ is $\left(\dfrac{1}{2},2\right)$. Let the area of the region enclosed by these curves be $\dfrac{1}{24}(l\sqrt{5}+m)-n\log_e(1+\sqrt{5})$, where $l,m,n\in\mathbb{N}$. Then $l+m+n$ is equal to:
Step-by-Step Solution
Key Concept: Find both intersection points, then integrate $(1+3x-2x^2-1/x)$ between them. Match coefficients.
$l+m+n=30$.
Correct Answer: 3