Exam Questions & Step-by-Step Markschemes (8 Problems)
Question 1 • 2024
5 Marks
Find the area of the region in the first quadrant enclosed by the x -axis, the line y = x , and the circle x^2 + y^2 = 32 .
Answer: A = 4\pi \text{ sq. units}
Question 2 • 2023
5 Marks
Find the area of the region bounded by the parabola y^2 = 4x and the line y = 2x .
Answer: A = \frac{1}{3} \text{ sq. units}
Question 3 • 2023
5 Marks
Find the area of the region bounded by the parabola y^2 = 4x and the straight line y = 2x .
Answer: \text{Area} = \frac{1}{3} \text{ sq. units}
Question 4 • 2024
5 Marks
Using integration, find the area bounded by the triangle with vertices (-1, 0), (1, 3) and (3, 2) .
Answer: \text{Area} = 4 \text{ sq. units}
Question 5 • 2023
5 Marks
Find the area of the region enclosed between the two parabolas y^2 = 4ax and x^2 = 4ay ( a > 0 ) using definite integration.
Answer: \text{Area} = \frac{16a^2}{3} \text{ sq. units}
Question 6 • 2024
3 Marks
Find the area of the region enclosed between the parabola y^2 = 4ax and its latus rectum x = a using integration.
Answer: \text{Area} = \frac{8}{3}a^2 \text{ sq. units}