# NCERT Class 12-Mathematics: Chapter – 8 Application of Integrals Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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