PYQSidePowered byPrepblink ExamsMy practice

Integrals

JEE Main 2024 (Online) 27th January Evening ShiftMCQMedium📈 Topic in 21% papers+4−1
Ques. 1JEE 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

Answer

(1) e ( | -1 (x3+ 1x3 ) | )1/3+C

Solution

Put t= -1 (x3+ 1x3 )

dt= 3 (x2- 1x4 )1+ (x3+ 1x3 )2 dx

= 3 (x6-1 )/x4 (x12+3x6+1 )/x6 dx

= 3 (x8-x2 )x12+3x6+1 dx

1+ (x3+ 1x3 )2= x12+3x6+1x6

I= 13 dtt= 13 |t|+C

= e | -1 (x3+ 1x3 ) |1/3+C

Answer: (1)

Keep practising — Integrals

Ques. 2JEE 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. 3JEE 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)