Advertisements
Advertisements
प्रश्न
Using integration finds the area of the region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2).
उत्तर
BL and CM are drawn perpendicular to x-axis.
It can be observed in the following figure that,
Area (ΔACB) = Area (ALBA) + Area (BLMCB) – Area (AMCA) … (1)
Therefore, from equation (1), we obtain
Area (ΔABC) = (3 + 5 – 4) = 4 units
APPEARS IN
संबंधित प्रश्न
Using integration, find the area of the region bounded by the triangle whose vertices are (−1, 2), (1, 5) and (3, 4).
Find the area of the region lying between the parabolas y2 = 4ax and x2 = 4ay.
Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y
Find the area of the region bounded by the curves y = x2 + 2, y = x, x = 0 and x = 3
Using integration find the area of the triangular region whose sides have the equations y = 2x +1, y = 3x + 1 and x = 4.
Smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2 is
A. 2 (π – 2)
B. π – 2
C. 2π – 1
D. 2 (π + 2)
Area lying between the curve y2 = 4x and y = 2x is
A. 2/3
B. 1/3
C. 1/4
D. 3/4
Using the method of integration find the area bounded by the curve |x| + |y| = 1 .
[Hint: The required region is bounded by lines x + y = 1, x– y = 1, – x + y = 1 and
– x – y = 1].
Find the area bounded by curves {(x, y) : y ≥ x2 and y = |x|}.
Choose the correct answer The area of the circle x2 + y2 = 16 exterior to the parabola y2 = 6x is
A. `4/3 (4pi - sqrt3)`
B. `4/3 (4pi + sqrt3)`
C. `4/3 (8pi - sqrt3)`
D.`4/3 (4pi + sqrt3)`
Using integration, find the area of region bounded by the triangle whose vertices are (–2, 1), (0, 4) and (2, 3).
The area enclosed between the curves y = loge (x + e), x = loge \[\left( \frac{1}{y} \right)\] and the x-axis is _______ .
Area enclosed between the curve y2 (2a − x) = x3 and the line x = 2a above x-axis is ___________ .
Solve the following :
Find the area of the region lying between the parabolas :
y2 = 4x and x2 = 4y
The area of the region included between the parabolas y2 = 16x and x2 = 16y, is given by ______ sq.units
The area enclosed between the two parabolas y2 = 20x and y = 2x is ______ sq.units
The area of triangle ΔABC whose vertices are A(1, 1), B(2, 1) and C(3, 3) is ______ sq.units
Find the area of the ellipse `x^2/1 + y^2/4` = 1, in first quadrant
Find the area of sector bounded by the circle x2 + y2 = 25, in the first quadrant−
Find the area enclosed between the X-axis and the curve y = sin x for values of x between 0 to 2π
Find the area of the ellipse `x^2/36 + y^2/64` = 1, using integration
Find the area of the region lying between the parabolas 4y2 = 9x and 3x2 = 16y
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 a minor segment of the circle x2 + y2 = a2 cut off by the line x = `"a"/2`
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.
Area lying between the curves `y^2 = 4x` and `y = 2x`
Using Integration, find the area of triangle whose vertices are (– 1, 1), (0, 5) and (3, 2).
