Balbharati Maharashtra State Board Std 12 Commerce Statistics Part 1 Digest Pdf Chapter 7 Application of Definite Integration Ex 7.1 Questions and Answers.

## Maharashtra State Board 12th Commerce Maths Solutions Chapter 7 Application of Definite Integration Ex 7.1

Question 1.

Find the area of the region bounded by the following curves, the X-axis, and the given lines:

(i) y = x^{4}, x = 1, x = 5

Solution:

(ii) y = \(\sqrt{6 x+4}\), x = 0, x = 2

Solution:

(iii) \(\sqrt{16-x^{2}}\), x = 0, x = 4

Solution:

(iv) 2y = 5x + 7, x = 2, x = 8

Solution:

(v) 2y + x = 8, x = 2, x = 4

Solution:

(vi) y = x^{2} + 1, x = 0, x = 3

Solution:

(vii) y = 2 – x^{2}, x = -1, x = 1

Solution:

Question 2.

Find the area of the region bounded by the parabola y^{2} = 4x and the line x = 3.

Solution:

Required area = area of the region OABO

= 2(area of the region OACO)

Question 3.

Find the area of the circle x^{2} + y^{2} = 25.

Solution:

By the symmetry of the circle, its area is equal to 4 times the area of the region OABO.

Clearly, for this region, the limits of integration are 0 and 5.

From the equation of the circle, y^{2} = 25 – x^{2}.

In the first quadrant y > 0

∴ y = \(\sqrt{25-x^{2}}\)

∴ area of the circle = 4(area of region OABO)

Question 4.

Find the area of the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{25}\) = 1

Solution:

By the symmetry of the ellipse, its area is equal to 4 times the area of the region OABO.

Clearly, for this region, the limits of integration are 0 and 2.

From the equation of the ellipse,