Find the Area of the Region Bounded by the Parabola

Area of OACO Area ΔOABArea OBACO. Since the approximating rectangle can move between x 0 and x a and as the parabola is symmetric about axis and as the parabola is symmetric about x axis Required shaded area OLSO Area OLMO Required shaded area OLSO A 2 Area OLMO.

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AskedMay 8 2021in Definite Integralsby Yajna300kpoints area of bounded regions.

. Let R be the region bounded by y 1x the lime x 1 the line x 3 and the x-axis. Find the area of the region bounded by the parabola y 24ax and its latus rectum. 18 and the x -axis.

Area of the region bounded by the parabola y 2 x 2 and the x -axis minus area of the triangle A B C. Find the area of the region bounded by the parabola y 3x2 the tangent line to this parabola at 1 3 and the x-axis. A The line x2 b The line x-1 c The x axis d The line.

Ex 81 9 Find the area of the region bounded by the parabola 2 and We know parabola is symmetric about its axis x2 y is symmetric about y axis Area of shaded region 2 Area of OBD First we find Point B Point B is point of intersection of y x parabola We know that Putting value of in. Y 2 16x and its latus rectum. The equation of the vertical line is x 3.

Asked1 dayagoin Mathematicsby Sowaiba712kpoints Find the area of the region bounded by. 2 area of the region OPBO where 2 y d x where y 4 - x 2. Solution Verified by Toppr Parabola is y 2x and line is xy2 Solving both x2y y 2x y 22y y 2y20 y 22yy20 yy21y20 y1y20 y12 Area included between line and parabola is the area of shaded region y 1 y 2 xdy 21 2yy 2dy 2y 2y 2 3y 3 21 2 21 31 42 98 67 310 67 310.

The parabola intersect the X-axis at A 2 0 and B 2 0 Required area area of he region APBOA. Sum Find the area of the region bounded by the parabola. The point of intersection of parabola x 2y and line yx is A11.

Concept Notes Videos 619. Equation of circle in standard form is x - α 2 y -. The region bounded by the parabola y 3x2 and the line y 12x - 12 and x - axis equation is y 0.

The area bounded by the parabola y2 4ax latus rectum and x-axis is A. 0 4 x 2. Find the area of the region bounded by the parabola y 5x2 the tangent line to this parabola at 5 125 and the x-axis.

MCQ Online Tests 60. Maharashtra State Board HSC Science Electronics 12th Board Exam Question Papers 185. For points of intersection of the parabola with X-axis we put y 0 in its equation.

CH61 Problem 48E Find the area of the region bounded by the parabola y x2 the tangent line to this parabola at 1 1 and the x -axis. 12x - 12 0. Units bounded by the parabola yx2-1 the tangent at the point 23 to it and the y-axis is asked 4 days ago in Mathematics by Sowaiba 712k points class-12.

Question Bank Solutions 12204. Find the area of the region bounded by the parabola y 2 2x and the straight line x y 4. In this case f x 3x2 g x 12x - 12.

The given area is symmetrical about y -axis. Area OACO Area ODBO. The region bounded by the parabolas r t212 and r t12-12 for -2sts2 The area of the region is Type an exact answer using a as needed Question.

X 2. Tangent line meets the x axis at 1. Area of approximating rectangle Area of approximating rectangle y d x.

Use a line integral on the boundary to find the area of the following region. To find the area we need to integral. For coordinate of intersection points A or B.

Its not 6253 Calc 2 Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y x 2 and the parabola y x2 about the following lines. Find the length of the latus rectum of the parabola y2 16x. Area of the region bounded by the parabola y 2 x 2 the tangent line to this parabola at 3.

The area in sq. The area of the region bounded by the parabola y2 2x1 the tangent to the parabola at the point 2 3 and the X-axis is A 3 B 6 C 9 D 12 Hard Solution Verified by Toppr Correct option is C Given equation of parabola is y 24yx50 Then the equation of tangent at 2 3 is 3y2y3 2x2 50 2yx40 Required area is given by. Shaded region is required bounded region which is symmetrical about x-axis.

Example 6 Find the area of the region bounded by the two parabolas 𝑦𝑥2 and 𝑦2 𝑥 Drawing figure Here we have parabolas 𝑦2𝑥 𝑥2𝑦 Area required Area OABC Finding Point of intersection B Solving 𝑦2 𝑥 𝑥2 𝑦 Put 2 in 1 𝑦2 𝑥 𝑥2 2𝑥 𝑥4𝑥0. The line x k divides R into two regions of equal area. Hence area of required region 2 Area OADO Area DACD Note.

X 2 4. Solving y 2 2x and x y 4 we get y 2 2 y 4. The area bounded by the parabola x 2y and the line yx can be represented as.

The parabola yx2 and the line y x A. Find the area of the region bounded by the parabola y2 32x and its Latus rectum in first quadrant. Units class-12 applications-of-integrals Share It On FacebookTwitterEmail Please log inor registerto add a comment.

Medium Solution Verified by Toppr The equation of parabola is y 24ax ----- 1 Let O be the vertex S be. Advertisement Remove all ads Solution Comparing y 2 16x with y 2 4ax we get 4a 16 a 4 focus is S a 0 4 0 For y 2 16x y 4 x Required area area of the region OBSAO 2 area of the region OSAO where 2 0 4 y d x where y 4 x. Advertisement Remove all ads Solution The parabola y 2 2x opens towards the positive x-axis and its focus is 1 2 0 The straight line x y 4 passes through 4 0 and 0 4.

Step-by-step solution 95 19 ratings for this solution Step 1 of 5 The equation of the parabola is The slope of the tangent at any point of the parabola The slope of the tangent at 1 1 is. F x g x Area is 7 square units.

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