# 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 *.*

**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 cos*t*, *.*

**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 .

**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 .

**Answer:**

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

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

Required area area of ABCD