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 .
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, .
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 .
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 .
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