Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board chapter 7 - Applications of Definite Integration [Latest edition]

Find the area of the region bounded by the following curves, the X-axis and the given lines:  y = x⁴, x = 1, x = 5

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = `sqrt(6x + 4), x = 0, x = 2`

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = `sqrt(16 - x^2)`, x = 0, x = 4

Find the area of the region bounded by the following curves, the X-axis and the given lines:  2y = 5x + 7, x = 2, x = 8

Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x² + 1, x = 0, x = 3

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = 2 – x², x = – 1, x = 1

Find the area of the region bounded by the parabola y² = 4x and the line x = 3.

Find the area of circle x² + y² = 25.

Find the area of ellipse `x^2/(4) + y^2/(25)` = 1.

Choose the correct alternative :

Area of the region bounded by the curve x² = y, the X-axis and the lines x = 1 and x = 3 is _______.

Choose the correct alternative :

The area of the region bounded by y² = 4x, the X-axis and the lines x = 1 and x = 4 is _______.

Choose the correct alternative :

Area of the region bounded by x² = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.

Choose the correct alternative :

Area of the region bounded by y = x⁴, x = 1, x = 5 and the X-axis is _____.

Choose the correct alternative :

Using definite integration, area of circle x² + y² = 25 is _______.

Fill in the blank : 

Area of the region bounded by y = x⁴, x = 1, x = 5 and the X-axis is _______.

Using definite integration, area of the circle x² + y² = 49 is _______.

Fill in the blank :

Area of the region bounded by x² = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.

Fill in the blank :

The area of the region bounded by the curve x² = y, the X-axis and the lines x = 3 and x = 9 is _______.

Fill in the blank :

The area of the region bounded by y² = 4x, the X-axis and the lines x = 1 and x = 4 is _______.

State whether the following is True or False :

The area bounded by the curve x = g (y), Y-axis and bounded between the lines y = c and y = d is given by `int_"c"^"d"x*dy = int_(y = "c")^(y = "d") "g"(y)*dy` 

State whether the following is True or False :

The area bounded by the two cures y = f(x), y = g (x) and X-axis is `|int_"a"^"b" f(x)*dx - int_"b"^"a" "g"(x)*dx|`.

State whether the following is True or False :

The area bounded by the curve y = f(x), X-axis and lines x = a and x = b is `|int_"a"^"b" f(x)*dx|`.

State whether the following is True or False :

If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b is positive.

State whether the following is True or False :

The area of the portion lying above the X-axis is positive.

Solve the following :

Find the area of the region bounded by the curve xy = c², the X-axis, and the lines x = c, x = 2c.

Solve the following :

Find the area between the parabolas y² = 7x and x² = 7y.

Solve the following :

Find the area of the region bounded by the curve y = x² and the line y = 10.

Solve the following :

Find the area of the ellipse `x^2/(16) + y^2/(9)` = 1.

Solve the following :

Find the area of the region bounded by y = x², the X-axis and x = 1, x = 4.

Solve the following :

Find the area of the region bounded by the curve x² = 25y, y = 1, y = 4 and the Y-axis.

Solve the following :

Find the area of the region bounded by the parabola y² = 25x and the line x = 5.