NCERT Exemplar solutions for Mathematics [English] Class 12 chapter 8 - Application Of Integrals [Latest edition]

Find the area of the curve y = sin x between 0 and π.

Find the area of the region bounded by the curve ay² = x³, the y-axis and the lines y = a and y = 2a.

Find the area of the region bounded by the parabola y² = 2x and the straight line x – y = 4.

Find the area of the region bounded by the parabolas y² = 6x and x² = 6y.

Find the area enclosed by the curve x = 3 cost, y = 2 sint.

Find the area of the region included between the parabola y = `(3x^2)/4` and the line 3x – 2y + 12 = 0.

Find the area of the region bounded by the curves x = at² and y = 2at between the ordinate corresponding to t = 1 and t = 2.

Find the area of the region above the x-axis, included between the parabola y² = ax and the circle x² + y² = 2ax.

Find the area of a minor segment of the circle x² + y² = a² cut off by the line x = `"a"/2`

The area enclosed by the circle x² + y² = 2 is equal to ______.

The area enclosed by the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 is equal to ______.

The area of the region bounded by the curve y = x² and the line y = 16 ______.

The area of the region bounded by the curve x = y², y-axis and the line y = 3 and y = 4 is ______.

The area of the region bounded by the curve y = x² + x, x-axis and the line x = 2 and x = 5 is equal to ______.

Find the area of the region bounded by the curves y² = 9x, y = 3x

Find the area of the region bounded by the parabola y² = 2px, x² = 2py

Find the area of the region bounded by the curve y = x³ and y = x + 6 and x = 0

Find the area of the region bounded by the curve y² = 4x, x² = 4y.

Find the area of the region included between y² = 9x and y = x

Find the area of the region enclosed by the parabola x² = y and the line y = x + 2

Find the area of region bounded by the line x = 2 and the parabola y² = 8x

Sketch the region `{(x, 0) : y = sqrt(4 - x^2)}` and x-axis. Find the area of the region using integration.

Calcualte the area under the curve y = `2sqrt(x)` included between the lines x = 0 and x = 1

Using integration, find the area of the region bounded by the line 2y = 5x + 7, x- axis and the lines x = 2 and x = 8.

Draw a rough sketch of the curve y = `sqrt(x - 1)` in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5.

Determine the area under the curve y = `sqrt("a"^2 - x^2)` included between the lines x = 0 and x = a.

Find the area of the region bounded by y = `sqrt(x)` and y = x.

Find the area enclosed by the curve y = –x² and the straight lilne x + y + 2 = 0

Find the area bounded by the curve y = `sqrt(x)`, x = 2y + 3 in the first quadrant and x-axis.

Find the area of the region bounded by the curve y² = 2x and x² + y² = 4x.

Find the area bounded by the curve y = sinx between x = 0 and x = 2π.

Find the area of region bounded by the triangle whose vertices are (–1, 1), (0, 5) and (3, 2), using integration.

Draw a rough sketch of the region {(x, y) : y² ≤ 6ax and x 2 + y² ≤ 16a²}. Also find the area of the region sketched using method of integration.

Compute the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.

Find the area bounded by the lines y = 4x + 5, y = 5 – x and 4y = x + 5.

Find the area bounded by the curve y = 2cosx and the x-axis from x = 0 to x = 2π

Draw a rough sketch of the given curve y = 1 + |x +1|, x = –3, x = 3, y = 0 and find the area of the region bounded by them, using integration.

The area of the region bounded by the y-axis, y = cosx and y = sinx, 0 ≤ x ≤ `pi/2` is ______.

The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is ______.

The area of the region bounded by the curve y = `sqrt(16 - x^2)` and x-axis is ______.

Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x² + y² = 32 is ______.

Area of the region bounded by the curve y = cosx between x = 0 and x = π is ______.

The area of the region bounded by parabola y² = x and the straight line 2y = x is ______.

The area of the region bounded by the curve y = sinx between the ordinates x = 0, x = `pi/2` and the x-axis is ______.

The area of the region bounded by the ellipse `x^2/25 + y^2/16` = 1 is ______.

The area of the region bounded by the circle x² + y² = 1 is ______.

The area of the region bounded by the curve y = x + 1 and the lines x = 2 and x = 3 is ______.

The area of the region bounded by the curve x = 2y + 3 and the y lines. y = 1 and y = –1 is ______.