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

The area of the region bounded by the curve y2 = 4x, the X axis and the lines x = 1 and x = 4 is ______

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प्रश्न

The area of the region bounded by the curve y2 = 4x, the X axis and the lines x = 1 and x = 4 is ______

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उत्तर

`56/3` sq.units

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.7: Application of Definite Integration - Q.1 (C)

संबंधित प्रश्‍न

Using integration find the area of the region {(x, y) : x2+y2⩽ 2ax, y2⩾ ax, x, y ⩾ 0}.


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 ellipse  `x^2/16 + y^2/9 = 1.`


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


Find the area of the smaller region bounded by the ellipse `x^2/a^2 + y^2/b^2 = 1` and the line `x/a + y/b =   1`


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


Using integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.


Find the area of the smaller region bounded by the ellipse \[\frac{x^2}{9} + \frac{y^2}{4} = 1\] and the line \[\frac{x}{3} + \frac{y}{2} = 1 .\]


Find the area of the region. 

{(x,y) : 0 ≤ y ≤ x2 , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .


Find the area of the region bounded by the following curve, the X-axis and the given line:

y = 2 – x2, x = –1, x = 1


Choose the correct alternative :

Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _____.


Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.


State whether the following is True or False :

The area bounded by the two cures y = f(x), y = g (x) and X-axis is `|int_"a"^"b" f(x)*dx - int_"b"^"a" "g"(x)*dx|`.


Solve the following :

Find the area of the region bounded by the curve y = x2 and the line y = 10.


Choose the correct alternative:

Area of the region bounded by the curve y = x3, x = 1, x = 4 and the X-axis 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 of the circle x2 + y2 = 16 is ______


The area of the region lying in the first quadrant and bounded by the curve y = 4x2, and the lines y = 2 and y = 4 is ______


Find the area of the circle x2 + y2 = 62 


The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______


The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.


The ratio in which the area bounded by the curves y2 = 8x and x2 = 8y is divided by the line x = 2 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


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


Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is ______.


Area bounded by the curves y = `"e"^(x^2)`, the x-axis and the lines x = 1, x = 2 is given to be α square units. If the area bounded by the curve y = `sqrt(ℓ "n"x)`, the x-axis and the lines x = e and x = e4 is expressed as (pe4 – qe – α), (where p and q are positive integers), then (p + q) is ______.


Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.


What is the area of an elementary horizontal strip of length \[x\] and infinitesimally small width \[dy\]?


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