Mathematics - Define Integrals and Its Application

Question - 1

\(\int^2_0\ e^2\ dx\) is equal to

  • A \(e^2-1\)
  • B \(e^4-1\)
  • C \(e^3-e^2\)
  • D \(e-1\)

Question - 2

\(\int^{\pi/2}{tan^2\ x\over 1+tan^2\ x}dx\) is equal to

  • A \(\infty\)
  • B 0
  • C \(\pi\over4\)
  • D \(\pi\over2\)

Question - 3

\(\int^{\pi\over 4}_0{sin^2x.cos^2\ x\over (sin^3x+cos^3\ x)^2}dx\) is equal to

  • A \(1\over 6\)
  • B \(1\over 12\)
  • C \(1\over 4\)
  • D \(1\over 24\)

Question - 4

\(\int^{\pi\over 2}_0{sin^nx\over sin^nx+cos^nx}dx\) is equal to

  • A \(\pi\over 4\)
  • B \(\pi\over 2\)
  • C \(\pi\over 3\)
  • D \(\pi\over 6\)

Question - 5

The value of integral \(\int^{2\pi}_0e^x\ sin({{\pi\over 4}+{\pi\over 2}})dx\) is

  • A \({\sqrt2\over 5}(e^{2\pi+1})\)
  • B \({-\sqrt2\over 5}(e^{2\pi+1})\)
  • C \({-\sqrt2\over 5}(e^{2\pi-1})\)
  • D \({\sqrt2\over 5}(e^{2\pi-1})\)

Question - 6

\(\int^3_2\ {2x^5+x^4-2x^3+2x^2+1\over (x^2+1)(x^4-1)}dx\) is equal to

  • A \({1\over 2}({log6+{1\over5}})\)
  • B \({1\over 2}({log6-{1\over5}})\)
  • C \(-{1\over 2}({log6+{1\over5}})\)
  • D \({1\over 3}({log6-{1\over5}})\)

Question - 7

Find the value of \(\int^3_1|(x-1)(x-2)(x-3)|dx.\)

  • A \(1\over 3\)
  • B \(1\over 2\)
  • C \(9\over 4\)
  • D \(9\over 5\)

Question - 8

Find the value of \(\int^{/pi}_0\ {sin2kr\over sin\ x}dx\), where \(k\in I.\)

  • A \(\pi\over2\)
  • B \(\pi\)
  • C \(3\pi\over2\)
  • D 0

Question - 9

\(\int^{\pi/4}_0\ {sin\ x+cos\ x\over 9+16\ sin2x }dx\) is equal to

  • A \(in\ 3\over 20\)
  • B \(In\ 3\over 40\)
  • C \(In\ 3\over 60\)
  • D \(In\ 3\over 100\)

Question - 10

\(\int^{\pi}_0{x\ tan\ x\over sec\ x + tan\ x}dx\) is equal to 

  • A \({\pi\over 2}(\pi-2)\)
  • B \({\pi}(\pi-2)\)
  • C \({\pi\over 4}(\pi-2)\)
  • D \({\pi\over 4}(\pi+2)\)
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