JEE Main & Advanced Mathematics Definite Integration Question Bank

done Numerical Value Type Questions - Application of Integrals Total Questions - 15

• question_answer1)
  The area (in sq. units) bounded by the parabola \[y={{x}^{2}}-1,\] the tangent at the point \[(2,3)\] to it and the y-axis is
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• question_answer2)
  Let \[f(x)\] be a continuous function such that the area bounded by the curve \[y=f(x),\] x-axis and the lines \[x=0\] and \[x=a\] is \[\frac{{{a}^{2}}}{2}+\frac{a}{2}\sin a+\frac{\pi }{2}\cos a,\] then  is
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• question_answer3)
  The area of the region \[A=\{(x,y):0\le y\le x|x|+1\] and \[-1\le x\le 1\}\] in sq. units is
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• question_answer4)
  The area of the region bounded by the curves \[y=|x-2|,\] \[x=1,\] \[x=3\] and the x-axis is
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• question_answer5)
  The area (in sq. units) in the first quadrant bounded by the parabola, \[y={{x}^{2}}+1,\] the tangent to it at the point \[(2,5)\] and the coordinate axes is
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• question_answer6)
  Area of the square formed by \[|x|+|y|=1\] is
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• question_answer7)
  The area (in sq. units) of the region bounded by the parabola, \[y={{x}^{2}}+2\] and the lines, \[y=x+1,x=0\] and \[x=3,\] is
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• question_answer8)
  If area bounded by the curves \[{{y}^{2}}=4ax\] and \[y=mx\] is \[\frac{{{a}^{2}}}{3},\] then the value of m is
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• question_answer9)
  The area (in sq. units) of the region \[A=\{(x,y)\in R\times R|0\,\,d\le xd\le 3,\,\]\[0\,\,d\le y\,d\le 4,\,y\,\,d\le {{x}^{2}}+3x\}\] is
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• question_answer10)
  The area enclosed between the curve \[y={{\log }_{e}}(x+e)\] and the coordinate axes is
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• question_answer11)
  The area (in sq. units) of the region \[A=\{(x,y):{{x}^{2}}\le y\le x+2\}\] is
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• question_answer12)
  The area bounded by the curves \[y=lnx,\] \[y=ln|x|,\] \[y=|ln\,\,x|\] and \[y=|ln|x||\] is
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• question_answer13)
  The area (in sq. units) of the region \[A=\{(x,y):\frac{{{y}^{2}}}{2}\le x\le y+4\}\] is
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• question_answer14)
  If the area (in sq. units) of the region \[\{(x,y):{{y}^{2}}\le 4x,\,x+y\le 1,\,\,x\ge 0,\,y\ge 0\}\] is \[a\sqrt{2}+b,\] then \[a-b\] is equal to:
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• question_answer15)
  The area of the region bounded by the curves \[y=\left| x-1 \right|\] and \[y=3-\left| x \right|\] is
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