Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Integrals

Short Answer Type

91.

Evaluate the following integral using substitution.
$integral subscript 0 superscript 1 fraction numerator straight x over denominator straight x squared plus 1 end fraction dx$

97 Views

92.

Evaluate the following integral using substitution.

105 Views

93.

Evaluate the following definite integral:
$integral subscript 0 superscript 1 straight x space straight e to the power of straight x squared end exponent space dx$

108 Views

94.

Evaluate the following definite integral:
$integral subscript 1 superscript 2 fraction numerator 1 over denominator straight x left parenthesis 1 plus log space straight x right parenthesis squared end fraction dx$

97 Views

95.

Evaluate the following integral using substitution
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator sin space straight x over denominator 1 plus cos squared straight x end fraction dx$

132 Views

96.

Evaluate the following integral:
$integral subscript straight pi over 6 end subscript superscript straight pi over 2 end superscript fraction numerator cosec space straight x space cotx over denominator 1 minus cosec squared straight x end fraction dx$

110 Views

97.
Evaluate the following integral:
$integral subscript 1 superscript 2 1 over straight x squared straight e to the power of negative 1 over straight x end exponent dx$

Let I = $integral subscript 1 superscript 2 1 over straight x squared straight e to the power of 1 over straight x end exponent dx$
Put $1 over straight x space equals straight y comma space space space space space space therefore space space minus 1 over straight x squared dx space equals space dy space space space space space space space space space space rightwards double arrow space space space 1 over straight x squared dx space space equals negative dy$
When x = 1, y = 1
When x =2, y = $1 half$
$therefore space space space straight I space space equals negative integral subscript 1 superscript 1 half end superscript space straight e to the power of straight y space dx equals space minus open square brackets straight e to the power of straight y close square brackets subscript 1 superscript 1 half end superscript space equals space minus open square brackets straight e to the power of 1 half end exponent minus straight e to the power of 1 close square brackets space equals space straight e minus square root of straight e$

120 Views

98.

Evaluate the following integral:
$integral subscript 0 superscript 1 fraction numerator left parenthesis tan to the power of negative 1 end exponent straight x right parenthesis squared over denominator 1 plus straight x squared end fraction dx$

110 Views

99.

Evaluate the following integral using substitution.
$integral subscript 0 superscript 2 straight x space square root of straight x plus 2 end root dx.$

115 Views

100.

Evaluate $integral subscript negative 1 end subscript superscript 1 5 straight x to the power of 4 square root of straight x to the power of 5 plus 1 end root dx.$

104 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

97. Evaluate the following integral:

97.
Evaluate the following integral:
$integral subscript 1 superscript 2 1 over straight x squared straight e to the power of negative 1 over straight x end exponent dx$