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CBSE Questions for Class 12 Commerce Maths Application Of Integrals Quiz 3 - MCQExams.com

The area bounded by the circle x2+y2=8, the parabola x2=2y and the line y=x in y0 is
  • 23+2π
  • 232π
  • 23+π
  • 23π
The area bounded by the curve y=sinx and y=cosx,0xπ/2 is
  • 2(21)
  • 22(31)
  • 2(2+1)
  • 31
Area bounded by the curves y=xex and y=xex and the line |x|=1 is
  • 1
  • 4e
  • e
  • 1
The area common to the curves y2=x and x2=yis 
  • 1
  • 23
  • 13
  • None of these
The area bounded by y=x2 and y=1x2 is
  • 83
  • 163
  • 323
  • 173
The area bounded by |y|=1x2 is
  • 8/3
  • 4/3
  • 16/3
  • None of these
If y=(x) is the solution of equation ydx+dy=exy2dy,(0)=1 and area bounded by the curve  y=(x), y=ex and x=1 is A, then
  • curve y=(x) is passing through (2,e)
  • curve y=(x) is passing through (1,1e)
  • A=e2e+3
  • A=e+2e3
The area common to the circle x2+y2=16a2 and the parabola y2=6ax is
  • 4a23(4π3)
  • 4a23(8π3)
  • 4a23(4π+3)
  • None of these
The area of the region(s) enclosed by the curves y=x2 and y=|x| is:
  • 1/3
  • 2/3
  • 1/6
  • 1
Let 'a' be a positive constant number. Consider two curves C1:y=ex,C2:y=eax. Let S be the area of the part surrounded by C1,C2 and the y-axis, then
  • lim
  • \displaystyle \lim_{a\rightarrow 0}\frac{S}{a^{2}}=\frac{1}{4}
  • Range of S is \displaystyle \left ( 0, \infty \right )
  • S(a) is neither odd nor even
The area bounded by the curves x^2+y^2\le 8 and y^2\ge 4x lying  in the first quadrant is not equal to
  • \displaystyle 32\left( \frac { \pi  }{ 8 } -\frac1 3\right)
  • \displaystyle \frac { 32 }{ 3 } \left( \frac { 3\pi  }{ 8 } -1 \right)
  • \displaystyle 4\pi -\frac { 32 }{ 3 }
  • \displaystyle \frac { 1 }{ 3 } \left( 12\pi -32 \right)
Area enclosed by the curves \displaystyle y=\ln x;y=\ln\left | x \right |;y=\left | \ln x \right | and \displaystyle y=\left | \ln\left | x \right | \right | is equal to
  • 2
  • 4
  • 8
  • Cannot be determined
The area of the figure bounded by the lines x= 0,\: x= \dfrac{\pi}{2},\: f\left ( x \right )= \sin x and g\left ( x \right )= \cos x is
  • 2\left ( \sqrt{2}-1 \right )
  • \sqrt{3}-1
  • 2\left ( \sqrt{3}-1 \right )
  • 2\left ( \sqrt{2}+1 \right )
The area of the figure bounded by the curves \displaystyle y=\ln x\displaystyle y=\left ( \ln x \right )^{2} is
  • e+1
  • e-1
  • 3-e
  • 1
The area of the smaller portion between curves x^2 + y^2 = 8 and y^2 = 2x is
  • \displaystyle \pi + \frac{2}{3}
  • \displaystyle 2\pi + \frac{2}{3}
  • \displaystyle 2 \pi + \frac{4}{3}
  • \displaystyle \pi + \frac{4}{3}
Area bounded by \displaystyle y=2\sqrt { x } and x=3\sqrt { y }  is equal to (in sq. units) 
  • 12
  • 8
  • 10
  • 6
The area between the parabola y =x^2 and the line y = x is
  • \dfrac{1}{6} sq. units
  • \dfrac{1}{3} sq. units
  • \dfrac{1}{2} sq. units
  • None of these
Area lying in the first quadrant and bounded by the circle x^2 + y^2 = 4 and the lines x = 0 and x = 2 is
  • \pi
  • \dfrac {\pi}{2}
  • \dfrac {\pi}{3}
  • \dfrac {\pi}{4}
The area bounded by {y}^{2}=4x and {x}^{2}=4y is
  • \cfrac { 20 }{ 3 } sq. units
  • \cfrac { 16 }{ 3 } sq. units
  • \cfrac { 14 }{ 3 } sq. units
  • \cfrac { 10 }{ 3 } sq. units
The area of the region bounded by the y-axis, y = \cos x and y = \sin x, 0\leq x \leq \dfrac {\pi}{2} is
  • 2(\sqrt {2} - 1)
  • \sqrt {2} - 1
  • \sqrt {2}+ 1
  • \sqrt {2}
Area bounded between the curve x^2=y and the line y=4x is
  • \displaystyle\frac{32}{3}sq unit
  • \displaystyle\frac{1}{3}sq unit
  • \displaystyle\frac{8}{3}sq unit
  • \displaystyle\frac{16}{3}sq unit
The area enclosed between the curve \displaystyle y=1+{ x }^{ 2 }, the y-axis and the straight line \displaystyle y=5 is given by
  • \displaystyle \frac { 14 }{ 3 } sq unit
  • \displaystyle \frac { 7 }{ 3 } sq unit
  • \displaystyle 5 sq unit
  • \displaystyle \frac { 16 }{ 3 } sq unit
The area bounded by the parabolas y=4x^2,\,y=\dfrac{x^2}{9} and line y=2 is
  • \dfrac{5\sqrt{2}}{3} sq units
  • \dfrac{10\sqrt{2}}{3} sq units
  • \dfrac{15\sqrt{2}}{3} sq units
  • \dfrac{20\sqrt{20}}{3} sq units
The area of the circle x^2+y^2=16 exterior to the parabola y^2=6x is
  • \dfrac {4}{3}(4\pi -\sqrt 3)
  • \dfrac {4}{3}(4\pi +\sqrt 3)
  • \dfrac {4}{3}(8\pi -\sqrt 3)
  • \dfrac {4}{3}(8\pi +\sqrt 3)
The area bounded by the curve y=x|x|, x-axis and the ordinates x=-1 and x=1 is given by
  • 0
  • \dfrac {1}{3}
  • \dfrac {2}{3}
  • \dfrac {4}{3}
Area bounded by the curves y=x^3, the x-axis and the ordinates x=-2 and x=1 is
  • -9
  • -\dfrac {15}{4}
  • \dfrac {15}{4}
  • \dfrac {17}{4}
The area of the region bounded by the curves y={ x }^{ 2 } and x={ y }^{ 2 } is
  • \dfrac {1}{3}
  • \dfrac {1}{2}
  • \dfrac { 1 }{ 4 }
  • 3
Area of the region bounded by y = |x| and y = |x| + 2, is
  • 4\ sq. units
  • 3\ sq. units
  • 2\ sq. units
  • 1\ sq. units
The area included between the parabolas x^2=4y and y^2=4x is (in square units)
  • \dfrac{4}{3}
  • \dfrac{1}{3}
  • \dfrac{16}{3}
  • \dfrac{8}{3}
The area enclosed between the curves \displaystyle y={ x }^{ 3 } and \displaystyle y=\sqrt { x }  is, (in square units):
  • \displaystyle \frac { 5 }{ 3 }
  • \displaystyle \frac { 5 }{ 4 }
  • \displaystyle \frac { 5 }{ 12 }
  • \displaystyle \frac { 12 }{ 5 }
The area included between the parabolas \displaystyle { y }^{ 2 }=4x and \displaystyle { x }^{ 2 }=4y is
  • \displaystyle \frac { 8 }{ 3 } sq unit
  • \displaystyle 8 sq unit
  • \displaystyle \frac { 16 }{ 3 } sq unit
  • \displaystyle 12 sq unit
The area of the region bounded by the graph of y = \sin x and y = \cos x between x = 0 and x = \dfrac {\pi}{4} is
  • \sqrt {2} + 1
  • \sqrt {2} - 1
  • 2\sqrt {2} - 2
  • 2\sqrt {2} + 2
Area of the region satisfying x \le 2, y \le |x|,x-axis and x\ge 0 is:
  • 4 sq unit
  • 1 sq unit
  • 2 sq unit
  • None of these
The area of the region bounded by the curves y = x^{3}, y = \dfrac {1}{x}, x = 2 is
  • 4 - \log_{e}2
  • \dfrac {1}{4} + \log_{e}2
  • 3 - \log_{e}2
  • \dfrac {15}{4} - \log_{e}2
The area (in square units) bounded by the curves y^{2} = 4x and x^{2} = 4y is
  • \dfrac {64}{3}
  • \dfrac {16}{3}
  • \dfrac {8}{3}
  • \dfrac {2}{3}
The line 2y=3x+12 cuts the parabola 4y=3x^2What is the area enclosed by the parabola and the line?
  • 27 square unit
  • 36 square unit
  • 48 square unit
  • 54 square unit
The area in the first quadrant between x^2 + y^2 = \pi^2 and y = sin  x is
  • \dfrac{\pi^3 - 8}{4}
  • \dfrac{\pi^3}{4}
  • \dfrac{\pi^3 - 16}{4}
  • \dfrac{\pi^3 - 8}{2}
Consider the curves y = \sin x and y = \cos x.
What is the area of the region bounded by the above two curves and the lines x = 0 and x = \dfrac {\pi}{4}?
  • \sqrt {2} - 1
  • \sqrt {2} + 1
  • \sqrt {2}
  • 2
The area bounded by the curves y = \cos x and y = \sin x between the ordinates x = 0 and x = \dfrac {3\pi}{2} is
  • (4\sqrt {2} - 2)sq\ units
  • (4\sqrt {2} + 2)sq\ units
  • (4\sqrt {2} - 1)sq\ units
  • (4\sqrt {2} + 1)sq\ units
Consider the curves y = \sin x and y = \cos x.
What is the area of the region bounded by the above two curves and the lines x = \dfrac {\pi}{4} and x = \dfrac {\pi}{2}?
  • \sqrt {2} - 1
  • \sqrt {2} + 1
  • 2\sqrt {2}
  • 2
The area of the region bounded by the lines y = 2x + 1, y = 3x + 1 and x = 4 is
  • 16\ sq.unit
  • \dfrac {121}{3}\ sq.unit
  • \dfrac {121}{6}\ sq.unit
  • 8\ sq.unit
The area bounded by the curves y=\cos x and y=\sin x between the ordinates x=0 and x=\displaystyle\frac{3\pi}{2} is?
  • 4\sqrt{2}-1
  • 4\sqrt{2}+1
  • 4\sqrt{2}-2
  • 4\sqrt{2}+2
The line x=\dfrac{\pi}{4} divide the area of the region bounded by y=\sin x, y = \cos x and X-axis \left(0 \le x \le \frac{\pi}{2}\right) into two regions of areas A_1 and A_2. Then, A_1:A_2 equals
  • 4:1
  • 3:1
  • 2:1
  • 1:1
Area bounded by the curves y={ x }^{ 2 } and y=2-{ x }^{ 2 } is
  • \cfrac { 8 }{ 3 } sq. units
  • \cfrac { 3 }{ 8 } sq. units
  • \cfrac { 3 }{ 2 } sq. units
  • None of these
The area bounded by the parabola { y }^{ 2 }=4a(x+a) and { y }^{ 2 }=-4a(x-a) is
  • \cfrac { 16 }{ 3 } { a }^{ 2 }
  • \cfrac { 8 }{ 3 } { a }^{ 2 }
  • \cfrac { 4 }{ 3 } { a }^{ 2 }
  • None of these
Consider an ellipse \cfrac{x^2}{a^2}+\cfrac{y^2}{b^2}=1 What is the area included between the ellipse and the greatest rectangle inscribed in the ellipse?
  • ab(\pi -1)
  • 2ab(\pi -1)
  • ab(\pi -2)
  • None of the above
The area of the region bounded by the curve y = x^{2} and y = 4x - x^{2} is
  • \dfrac {16}{3}sq. units
  • \dfrac {8}{3}sq. units
  • \dfrac {4}{3}sq. units
  • \dfrac {2}{3}sq. units
The area of the figure bounded by the parabolas x = -2y^{2} and x = 1 - 3y^{2} is
  • \dfrac {4}{3} square units
  • \dfrac {2}{3} square units
  • \dfrac {3}{7} square units
  • \dfrac {6}{7} square units
The area formed by triangular shaped region bounded by the curves y=\sin { x } ,y=\cos { x } and x=0 is
  • \left( \sqrt { 2 } -1 \right) sq unit
  • 1 sq unit
  • \sqrt { 2 } sq units
  • \left( \sqrt { 2 } +1 \right) sq units
The area of the figure bounded by the curves y = |x - 1| and y = 3 - |x| is
  • 2\ sq. units
  • 3\ sq. units
  • 4\ sq. units
  • 1\ sq. units
0:0:1


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