Explanation
Solution
Step 1: Express the curves in terms of y
Step 2: Find the Points of Intersection
To find where the curves meet, set the x values equal to each other:
Multiply the entire equation by 4 to clear the fractions:
Rearrange into a quadratic equation:
Factor the quadratic:
The points of intersection are at y=−4 and y=2.
Step 3: Calculate the Area
We integrate with respect to y from −4 to 2:
Area=∫−42(xparabola−xline)dy
Area=∫−42[(1−4y2)−(2y−2)]dy
Simplify the integrand:
Perform the integration:
Apply the limits:
Area=37−(−320)=37+20=327=9
Correct Option: (A) 9