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

The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is bafdbagd∫abf(x)dx+∫abg(x) dx

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प्रश्न

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`

पर्याय

  • True

  • False

MCQ
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उत्तर

This statement is False.

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

संबंधित प्रश्‍न

Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2 + y2 = 32.


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


Find the area under the given curve and given line:

y = x2, x = 1, x = 2 and x-axis


Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`


Find the area enclosed between the parabola y2 = 4ax and the line y = mx


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


Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4 , 1), B (6, 6) and C (8, 4).


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 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:  2y = 5x + 7, x = 2, x = 8


Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant 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 curve y = f(x), X-axis and lines x = a and x = b is `|int_"a"^"b" f(x)*dx|`.


If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b is positive.


Choose the correct alternative:

Area of the region bounded by y2 = 16x, x = 1 and x = 4 and the X axis, lying in the first quadrant is ______


The area of the region bounded by the curve y2 = x and the Y axis in the first quadrant and lines y = 3 and y = 9 is ______


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


Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant


Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2


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


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


Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 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 of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.


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


Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.


The area bounded by the curve `y = 3/2sqrtx`, the line x = 1 and x-axis is ______ sq. units.


What is the total area bounded by \[y=f(x)\], the \[x\]-axis, and the ordinates \[x=a\] and \[x=b\], when the region is above the \[x\]-axis?


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