Balbharati Maharashtra State BoardStd 12 Commerce Statistics Part 1 Digest PdfChapter 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
Maharashtra Board Solution
Find the area of the region bounded by the following curves, the X-axis, and the given lines: (i) y = x4, x = 1, x = 5
Solution & Step-by-Step Answer:
(ii) y = , x = 0, x = 2
Solution:
(iii) , 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 = x2+ 1, x = 0, x = 3
Solution:
(vii) y = 2 – x2, x = -1, x = 1
Solution:
Question 2
Maharashtra Board Solution
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
Solution & Step-by-Step Answer:
Required area = area of the region OABO = 2(area of the region OACO)
Question 3
Maharashtra Board Solution
Find the area of the circle x2 + y2 = 25.
Solution & Step-by-Step Answer:
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, y2 = 25 – x2. In the first quadrant y > 0 ∴ y = ∴ area of the circle = 4(area of region OABO)
Question 4
Maharashtra Board Solution
Find the area of the ellipse = 1
Solution & Step-by-Step Answer:
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,
