Find the area of the region bounded by the curvea)Square unitsb)2πSquare unitsc)π/2Square unitsd)2/πSquare unitsCorrect answer is option 'A'. Can you explain this answer?

Question

Find the area of the region bounded by the curvea)Square unitsb)2&pi;Square unitsc)&pi;/2Square unitsd)2/&pi;Square unitsCorrect answer is option 'A'. Can you explain this answer?

Answer

We have,

y² = 2x and x² + y² = 4x

y² = 2x is parabola opening to the right of positive direction x-axis

x² + y² = 4x

⇒ (x - 2)² + y² = 4 which is circle having center at (2,0) and radius 2 units

Solving the curves we get,

When x = 0, y = 0 and when x = 2, y = ±2
Thus points of intersection are (0,0), (2,2) and (2,-2)

The graph is as shown in the following figure:

Similar Mathematics Doubts

The value of m > 0 for which of the area of the region bounded by the curvesy = x - x2 and the line y = mx equals 9/2 is ____________. Correct answer is '4'. Can you explain this answer?

Volume of the solid generated by revolving the region bounded by the lines x = 0 , x = 2 and the curve about the line y = 2 is equal to _______. Correct answer is '6.345'. Can you explain this answer?

The volume of the region in the first octant (x>=0,y>=0,z>=0) bounded by the cylinder x^2 y^2=4 and the plane z=2 and z y=4 equals?

Consider the region D in the yz plane bounded by the line y = 1/2 and the curve y2 z2 = 1, where y≥0. If the region D is revolved about the R3 z-axis in ¹, then the volume of the resulting solid is: а) л//3 b) 2π//3 c) π/3/2 d) π√3?

Determine the volume of the region that lies behind the plane x y z=8 and in front of the region in the yz-plane that is bounded by z=3/2 √y and z=3/4 y is?

Top Courses for Mathematics

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams