Advertisements
Advertisements
प्रश्न
Find the area between the curves y = x and y = x2
Advertisements
उत्तर
The required area is represented by the shaded area OBAO as
The points of intersection of the curves, y = x and y = x2, is A (1, 1).
We draw AC perpendicular to x-axis.
∴ Area (OBAO) = Area (ΔOCA) – Area (OCABO) … (1)
APPEARS IN
संबंधित प्रश्न
Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle
`x^2+y^2=4 at (1, sqrt3)`
Find the area of the region bounded by x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant.
Find the area of the region bounded by the curve y2 = 4x and the line x = 3
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.
Find the area enclosed between the parabola y2 = 4ax and the line y = mx
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis
Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4.
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 parabola y2 = 4x and the line x = 3.
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.
Solve the following :
Find the area of the region bounded by the curve y = x2 and the line y = 10.
Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______
Choose the correct alternative:
Area of the region bounded by the curve x2 = 8y, the positive Y-axis lying in the first quadrant and the lines y = 4 and y = 9 is ______
Choose the correct alternative:
Area of the region bounded by x = y4, y = 1 and y = 5 and the Y-axis lying in the first quadrant is ______
State whether the following statement is True or False:
The area bounded by the curve y = f(x) lies on the both sides of the X-axis is `|int_"a"^"b" "f"(x) "d"x| + |int_"b"^"c" "f"(x) "d"x|`
The area bounded by the parabola x2 = 9y and the lines y = 4 and y = 9 in the first quadrant is ______
The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis is ______
Find the area of the region bounded by the curve 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8
Find area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3
The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.
`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______
Area enclosed between the curve y2(4 - x) = x3 and line x = 4 above X-axis is ______.
If a2 + b2 + c2 = – 2 and f(x) = `|(1 + a^2x, (1 + b^2)x, (1 + c^2)x),((1 + a^2)x, 1 + b^2x, (1 + c^2)x),((1 + a^2)x, (1 + b^2)x, 1 + c^2x)|` then f(x) is a polynomial of degree
Area bounded by y = sec2x, x = `π/6`, x = `π/3` and x-axis is ______.
The figure shows as triangle AOB and the parabola y = x2. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x2 is equal to ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
If the area enclosed by y = f(x), X-axis, x = a, x = b and y = g(x), X-axis, x = a, x = b are equal, then f(x) = g(x).
Which expression gives physical area when the curve \[y=f(x)\] lies below the \[x\]-axis from \[x=a\] to \[x=b\]?
Why cannot a curve crossing the \[x\]-axis within \[a,b\] be integrated directly from \[a\] to \[b\] to obtain total area?
Why is \[y\] taken as positive for the region AOBA of the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?
Which integral represents the enclosed area of the ellipse after using the positive first-quadrant value of \[y\]?
Which antiderivative is used in evaluating \[\int \sqrt{a^2-x^2}\,dx\] for the ellipse area?
What is the area enclosed by the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?
