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

The area bounded by the parabola x2 = 9y and the lines y = 4 and y = 9 in the first quadrant is ______

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प्रश्न

The area bounded by the parabola x2 = 9y and the lines y = 4 and y = 9 in the first quadrant is ______

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उत्तर

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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 in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.


Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis


Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.


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


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(16 - x^2)`, x = 0, x = 4


Find the area of the region bounded by the following curves, the X-axis and the given lines:

y = x2 + 1, x = 0, x = 3


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


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|`


State whether the following statement is True or False:

The equation of the area of the circle is `x^2/"a"^2 + y^2/"b"^2` = 1


Find the area of the region bounded by the curve y = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3


Find the area of the region bounded by the curve y = `sqrt(36 - x^2)`, the X-axis lying in the first quadrant and the lines x = 0 and x = 6


The area of the region bounded by the curve y = 4x3 − 6x2 + 4x + 1 and the lines x = 1, x = 5 and X-axis is ____________.


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 ______.


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


The area enclosed by the parabolas x = y2 - 1 and x = 1 - y2 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).


What is the area of an arbitrary elementary vertical strip of height \[y\] and width \[dx\]?


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


Which antiderivative is used in evaluating \[\int \sqrt{a^2-x^2}\,dx\] for the ellipse area?


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