NCERT Class 12-Mathematics: Chapter –8 Application of Integrals Part 2

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Question 4:

Find the area of the region bounded by the parabolas and .

Fig.8.4-Find the area of the region bounded by the parabolas

Find the Area of the Region Bounded by the Parabolas

Answer:

The intersecting points of the given parabolas are obtained by solving these equations for and , which are and . Hence

Question 5:

Find the area enclosed by the curve cost, .

Fig.8.5.-Find the area enclosed by the curve

Find the Area Enclosed by the Curve

Answer:

Eliminating as follows:

which is the equation of an ellipse.

From Fig. 8.5, we get the required area

Long Answer (L.A.)

Question 6:

Find the area of the region included between the parabola and the line .

Fig.8.6-Find the area of the region included between the par …

Find the Area of the Region Included between the Parabola

Answer:

Solving the equations of the given curves we get

which give

From Fig.8.6, the required area area of ABC

Question 7:

Find the area of the region bounded by the curves and at between the ordinate corresponding to and .

Fig.8.7-Find the area of the region bounded by the curves

Find the Area of the Region Bounded by the Curves

Answer:

Given that x = at2 ... (i), y = 2at ... (ii) ⇒ t = 2y a putting the value of t in (i), we get y2 = 4ax

Putting t = 1 and t = 2 in (i), we get x = a, and x = 4a

Required area area of ABCD

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