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

201.

Evaluate:
$integral subscript 0 superscript straight pi fraction numerator straight x space over denominator 1 plus sinx end fraction dx space equals space straight pi$

119 Views

202.

Show that:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator straight x space dx over denominator sinx space plus space cosx end fraction space equals space fraction numerator straight pi over denominator 2 square root of 2 end fraction log left parenthesis square root of 2 plus 1 right parenthesis$

120 Views

Long Answer Type

203.

Show that:
$integral subscript 0 superscript straight pi over 2 end superscript fraction numerator sin squared straight x over denominator sin space straight x space plus space cos space straight x end fraction space equals space fraction numerator 1 over denominator square root of 2 end fraction log left parenthesis square root of 2 plus 1 right parenthesis$

146 Views

Short Answer Type

204.

Show that:
$integral subscript 0 superscript straight pi fraction numerator straight x space tanx over denominator secx space cosecx end fraction space equals space straight pi squared over 4$

101 Views

205.

Show that:
$integral subscript 0 superscript straight pi fraction numerator straight x space tanx over denominator secx plus tanx end fraction dx space equals space straight pi open parentheses straight pi over 2 minus 1 close parentheses$

119 Views

Long Answer Type

206.

Show that:
$integral subscript 0 superscript 1 log space open parentheses 1 over straight x minus 1 close parentheses dx space equals space 0$

139 Views

Short Answer Type

207.
By using the properties of definite integrals, evaluate the following integral:
$integral subscript 0 superscript straight pi fraction numerator dx over denominator 1 plus sinx end fraction space equals space 2$

Let I = $integral subscript 0 superscript straight pi fraction numerator dx over denominator 1 plus sinx end fraction space equals space integral subscript 0 superscript straight pi fraction numerator dx over denominator 1 plus sinx end fraction cross times fraction numerator 1 minus sinx over denominator 1 minus sinx end fraction dx space equals space straight x integral subscript 0 superscript straight pi fraction numerator 1 minus sinx over denominator 1 minus sin squared straight x end fraction dx$
$equals space integral subscript 0 superscript straight pi fraction numerator 1 minus sinx over denominator cos squared straight x end fraction dx space equals space integral subscript 0 superscript straight pi open parentheses fraction numerator 1 over denominator cos squared straight x end fraction minus fraction numerator sinx over denominator cos squared straight x end fraction close parentheses dx space equals space integral subscript 0 superscript straight pi open parentheses fraction numerator 1 over denominator cos squared straight x end fraction minus 1 over cosx. sinx over cosx close parentheses dx$
$space equals space integral subscript 0 superscript straight pi left parenthesis sec squared straight x minus secx space tanx right parenthesis space dx space equals space open square brackets tanx space minus secx close square brackets subscript 0 superscript straight pi space equals space open square brackets left parenthesis tanπ minus secπ right parenthesis space minus space left parenthesis tan space 0 space minus space sec space 0 right parenthesis close square brackets space equals space open square brackets left parenthesis 0 plus 1 right parenthesis space minus space left square bracket 0 minus 1 right parenthesis close square brackets space equals space 2$

135 Views

208.

Show that:
$integral subscript 0 superscript straight pi space straight x space. space log space sinx space dx space equals space minus straight pi squared over 2 log space 2$

100 Views

209.

Show that:
$integral subscript 0 superscript straight pi over 2 end superscript open parentheses fraction numerator straight theta over denominator sin space straight theta end fraction close parentheses squared space dθ space equals space straight pi space log space 2$

153 Views

210.

Show that:
$integral subscript 0 superscript straight pi fraction numerator straight x space sinx over denominator 1 plus cos squared straight x end fraction dx space equals space straight pi squared over 4$