Area Under the Curve
Area with Parameter
nta_pyq_2024_apr
Grade 12
Question:
If the area of the region $\left\{(x,y):\dfrac{a}{x^2}\leq y\leq\dfrac{1}{x},\ 1\leq x\leq2,\ 0<a<1\right\}$ is $(\log_e 2)-\dfrac{1}{7}$, then the value of $7a-3$ is equal to:
Step-by-Step Solution
Key Concept: $\int_1^2(1/x-a/x^2)dx=\ln2-a/2=\ln2-1/7\Rightarrow a=2/7$.
$a=2/7$. $7a-3=-1$.
Correct Answer: 3