JEE Main & Advanced Mathematics Definite Integration Question Bank

done Numerical Value Type Questions - Area Under The Curve Total Questions - 15

• question_answer1)
  Find the area between the curve \[y=1-\left| x \right|\]and x-axis.
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• question_answer2)
  Find the area of the region enclosed between the curve \[{{x}^{2}}=2y\] and the straight line \[y\text{ }=\text{ }2.\]
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• question_answer3)
  Find the common area of the curves \[y=\sqrt{x}\] and \[x=\sqrt{y}\].
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• question_answer4)
  Find the area bounded by the curve \[y=\sin \,x,\] x-axis and the lines \[x=0\] and \[x=\pi \].
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• question_answer5)
  Find the area between the parabola \[{{x}^{2}}=4y\] and line \[x=4y-2.\]
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• question_answer6)
  Find the area of the region bounded by curves \[y=\left| x-1 \right|\]and \[y=3-\left| x \right|.\]
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• question_answer7)
  Find the area bounded by the curve \[y={{x}^{3}},\] x-axis and ordinates \[x=-2\] and \[x\text{ }=\text{ }1.\]
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• question_answer8)
  Find the area of the figure bounded by \[{{y}^{2}}=9x\] and \[y=3x.\]
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• question_answer9)
  If the area of the region\[\left\{ \left( x,y \right):{{x}^{2}}+{{y}^{2}}\,\,\le \,\,1\,\,\le \,\,x+y \right\},\] is \[\frac{\pi }{4}-k\] then find k.
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• question_answer10)
  If area bounded by the curve \[x{{y}^{2}}={{a}^{2}}\left( a-x \right)\]and the y-axis is \[k{{a}^{2}}\]then find k.
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• question_answer11)
  If the area bounded by the curves \[y={{e}^{x}},y={{e}^{-x}}\] and \[y=2,\], is \[2\log \left( \frac{k}{e} \right)\] then find k.
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• question_answer12)
  Find the area bounded by the curves \[y=\left| x-2 \right|,x=1,x=3\]and x-axis.
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• question_answer13)
  If the area bounded by the curves \[y=\sin x,y=\cos x\] and y-axis in first quadrant is \[\left( \sqrt{k}-1 \right)\] then find k.
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• question_answer14)
  Find the area bounded by region \[\left\{ \left( x,y \right):\,\,\left| x \right|\,\,\underline{>}\,\,y\,\,\underline{>}\,{{x}^{2}} \right\}.\]
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• question_answer15)
  Find the area bounded by loop of \[\left| y \right|=\sin \,\,x\] for \[0\,\,\le \,\,x\,\,\le \,\,\pi .\]
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