UPSC NDA I 2025 Mathematics Paper

Given,
The equation of the curve is y=4x, and the line x=4 intersects the curve at the point (4,16). We need to find the area bounded by the curve, the x-axis, and the line x=4.
The region of interest is a right triangle with a base along the x-axis from x=0 to x=4 and a height of 16 units, corresponding to the point (4,16).
The area of the triangle is given by the formula:
Area =‌

1

2

× base × height
Substituting the values of the base ( 4 units) and the height ( 16 units):
Area =‌

1

2

×4×16=32 square units
∴ The area is 32 square units.