Advertisements
Advertisements
प्रश्न
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = π
उत्तर
The curve y = sin x intersects the X-axis at x = 0 and x = π between x = 0 and x = π.
Two bounded regions A1 and A2 are obtained. Both the regions have equal areas.
∴ required area = A1 + A2 = 2A1
= `2 int_0^(pi/2) y*dx, "where" y = sin x`
= `2int_0^(pi/2) sinx*dx`
= `2[- cos x]_0^(pi/2)`
= `2[- cos pi/2 cos 0]`
= 2(– 0 + 1)
= 2 sq units.
APPEARS IN
संबंधित प्रश्न
Find the area of the region bounded by the following curves, X-axis and the given lines: x = 2y, y = 0, y = 4
Find the area of the region bounded by the following curves, X-axis and the given lines : y = sin x, x = 0, x = `pi/(2)`
Find the area of the region bounded by the following curves, X-axis and the given lines: xy = 2, x = 1, x = 4
Find the area of the region bounded by the parabola y2 = 16x and its latus rectum.
Find the area of the region bounded by the parabola: y = 4 – x2 and the X-axis.
Find the area of the region included between y2 = 2x and y = 2x.
Find the area of the region included between: y2 = 4x, and y = x
Find the area of the region included between: y2 = 4ax and the line y = x
Choose the correct option from the given alternatives :
The area bounded by the curve y = x3, the X-axis and the lines x = – 2 and x = 1 is
Choose the correct option from the given alternatives :
The area bounded by the parabola y2 = 8x, the X-axis and the latus rectum is
Choose the correct option from the given alternatives :
The area under the curve y = `2sqrt(x)`, enclosed between the lines x = 0 and x = 1 is
Choose the correct option from the given alternatives :
The area of the circle x2 + y2 = 25 in first quadrant is
Choose the correct option from the given alternatives :
The area of the region bounded by the ellipse `x^2/a^2 + y^2/b^2` = 1 is
Choose the correct option from the given alternatives :
The area bounded by the ellipse `x^2/a^2 y^2/b^2` = 1 and the line `x/a + y/b` = 1 is
Choose the correct option from the given alternatives :
The area enclosed between the two parabolas y2 = 4x and y = x is
The area bounded by the curve y = tan x, X-axis and the line x = `pi/(4)` is ______.
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : 0 ≤ x ≤ 5, 0 ≤ y ≤ 2
Solve the following :
Find the area of the region in first quadrant bounded by the circle x2 + y2 = 4 and the X-axis and the line x = `ysqrt(3)`.
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = `pi/(3)`
Solve the following :
Find the area of the region lying between the parabolas : 4y2 = 9x and 3x2 = 16y
Solve the following :
Find the area of the region lying between the parabolas : y2 = x and x2 = y.
Solve the following :
Find the area of the region bounded by the curve (y – 1)2 = 4(x + 1) and the line y = (x – 1).
The area of the region bounded by the curve y = sinx, X-axis and the lines x = 0, x = 4π is ______ sq.units
The area bounded by the parabola y2 = 32x the X-axis and the latus rectum is ______ sq.units
The area bounded by the ellipse `x^2/4 + y^2/25` = 1 and the line `x/2 + y/5` = 1 is ______ sq.units
Find the area bounded by the curve y2 = 36x, the line x = 2 in first quadrant
Find the area of the region bounded by the parabola y2 = 32x and its Latus rectum in first quadrant
Find the area of the region bounded by the curve y2 = 8x, the X−axis and the given lines x = 1, x = 3, y ≥ 0
Find the area of the region bounded by the curve x2 = 12y, the Y−axis and the given lines y = 2, y = 4, x ≥ 0
Using integration, find the area of the region bounded by the line 2y + x = 8 , X−axis and the lines x = 2 and x = 4
Find the area of the region bounded by the parabola x2 = 4y and The X-axis and the line x = 1, x = 4
Find the area of the region bounded by the curves x2 = 8y, y = 2, y = 4 and the Y-axis, lying in the first quadrant
Find the area of the region bounded by the curve (y − 1)2 = 4(x + 1) and the line y = (x − 1)
Find the area of the region bounded by the curve y2 = 4x, the X-axis and the lines x = 1, x = 4 for y ≥ 0.
Find the area common to the parabola y2 = x – 3 and the line x = 5.
