PYQSidePowered byPrepblink ExamsMy practice

Integrals

JEE Main 2024 (Online) 29th January Morning ShiftMCQHard📈 Topic in 3% papers+4−1
Ques. 1JEE Main 2024, 29 January (Morning Shift)

For x (- 2, 2 ), if y(x)= cosec x+ xcosec x x+ x 2x dx, and x ( 2 )-y(x)=0 then y ( 4 ) is equal to

  1. - 1 2 -1 ( 1 2 )
  2. -1 ( 1 2 )
  3. 12 -1 ( 1 2 )
  4. 1 2 -1 (- 12 )

Answer

(4) 1 2 -1 (- 12 )

Solution

Multiply numerator and denominator by x x:

Integrand = (1+ 2x) x1+ 4x

Put x=t: y= 1+t21+t4 dt= 1+ 1t2 (t- 1t )2+2 dt

Put t- 1t=u, (1+ 1t2 )dt=du:

y= duu2+2= 1 2 -1 ( t- 1t 2 )+C

x ( 2 )-: t 1, u 0 C=0

x= 4: t= 1 2, t- 1t=- 1 2

y ( 4 )= 1 2 -1 (- 12 )

Answer: (4)

Keep practising — Integrals

Ques. 2JEE Main 2024, 29 January (Morning Shift)

If the value of the integral - 2 2 ( x2 x1+ x+ 1+ 2x1+e x2023 )dx= 4( +a)-2, then the value of a is

  1. - 32
  2. 3
  3. 32
  4. 2
Ques. 3JEE Main 2024, 29 January (Evening Shift)

If 32x+ 32x 3x 3x (x- ) dx =A x- +B - x+C, where C is the integration constant, then AB is equal to

  1. 2
  2. 8 cosec(2 )
  3. 4 cosec(2 )
  4. 4
Ques. 4JEE Main 2024, 29 January (Evening Shift)

If /6 /3 1- 2x dx= + 2+ 3, where , and are rational numbers, then 3 +4 - is equal to .

Ques. 5JEE Main 2024, 27 January (Morning Shift)

If 01 1 3+x+ 1+x dx=a+b 2+c 3, where a, b, c are rational numbers, then 2a+3b-4c is equal to :

  1. 10
  2. 7
  3. 4
  4. 8
Ques. 6JEE Main 2024, 27 January (Morning Shift)

If (a, b) be the orthocentre of the triangle whose vertices are (1,2),(2,3) and (3,1), and I1= ab x (4x-x2 )dx, I2= ab (4x-x2 )dx, then 36 I1I2 is equal to :

  1. 80
  2. 72
  3. 66
  4. 88
Ques. 7JEE Main 2024, 27 January (Evening Shift)

The integral (x8-x2 )dx (x12+3x6+1 ) -1 (x3+ 1x3 ) is equal to :

  1. e ( | -1 (x3+ 1x3 ) | )1/3+C
  2. e ( | -1 (x3+ 1x3 ) | )+C
  3. e ( | -1 (x3+ 1x3 ) | )1/2+C
  4. e ( | -1 (x3+ 1x3 ) | )3+C
Ques. 8JEE Main 2024, 27 January (Evening Shift)

For 0<a<1, the value of the integral 0 dx1-2a x+a2 is :

  1. 2 +a2
  2. 2 -a2
  3. 1-a2
  4. 1+a2
Ques. 9JEE Main 2024, 27 January (Evening Shift)

Let f(x)= 0x g(t) e ( 1-t1+t )dt, where g is a continuous odd function. If - /2 /2 (f(x)+ x2 x1+ex )dx= ( )2- , then is equal to .

All Integrals PYQs →

PDFDownload Integrals PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇
All JEE Main Mathematics chapters
Class 11SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial TheoremSequences and SeriesStraight LinesConic SectionsIntroduction to Three Dimensional GeometryLimits and DerivativesStatisticsProbability
Class 12Relations and Functions (Class 12)Inverse Trigonometric FunctionsMatricesDeterminantsContinuity and DifferentiabilityApplication of DerivativesIntegralsApplication of IntegralsDifferential EquationsVector AlgebraThree Dimensional GeometryProbability (Class 12)