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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______

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प्रश्न

The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______

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उत्तर

`4/2(2sqrt(2) - 1)`

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पाठ 1.7: Application of Definite Integration - Q.1 (C)

संबंधित प्रश्‍न

Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.


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 parabola y = x2 and y = |x| .


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


Find the area under the given curve and given line:

y = x2, x = 1, x = 2 and x-axis


Find the area bounded by the circle x2 + y2 = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.


Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`


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:  2y = 5x + 7, x = 2, x = 8


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 _______.


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|`.


Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______


State whether the following statement is True or False:

The area of portion lying below the X axis is negative


The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x)  "d"x`


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


Find the area of the region bounded by the curve y = `sqrt(2x + 3)`, the X axis and the lines x = 0 and x = 2


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 the area of the region bounded by the curve y = (x2 + 2)2, the X-axis and the lines x = 1 and x = 3


Find the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5


The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.


Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:


The area (in sq.units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is ______.


The area (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} is ______.


The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.


Which integral gives the area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\]?


For the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\], which expression for \[y\] is obtained before selecting the first-quadrant branch?


Why is \[y\] taken as positive for the region AOBA of the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?


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