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

41.

Evaluate the following definite integral
$integral subscript 0 superscript straight pi over 4 end superscript space sin space 2 straight x space dx$

96 Views

42.

Evaluate the following definite integral
$integral subscript straight pi over 6 end subscript superscript straight pi over 4 end superscript space cosec space straight x space dx$

96 Views

43.

Evaluate the following definite integral
$integral subscript 4 superscript 5 straight e to the power of straight x dx$

128 Views

44.

Evaluate the following definite integral
$integral subscript 0 superscript straight pi over 4 end superscript space left parenthesis 2 sec squared straight x plus straight x cubed plus 2 right parenthesis dx$

93 Views

45.

Evaluate the following definite integral
$integral subscript 0 superscript straight pi over 4 end superscript left parenthesis 2 sec squared straight x plus straight x cubed plus 2 right parenthesis space dx$

92 Views

46.

Evaluate the following definite integral
$integral subscript 0 superscript straight pi open parentheses sin squared straight x over 2 minus cos squared straight x over 2 close parentheses space dx$

99 Views

47.
Evaluate the following definite integral
$integral subscript 1 superscript 2 left parenthesis 4 straight x cubed minus 5 straight x squared plus 6 straight x plus 9 right parenthesis space dx.$

Let I = $integral subscript 1 superscript 2 left parenthesis 4 straight x cubed minus 5 straight x squared plus 6 straight x plus 9 right parenthesis space dx$
$equals space open square brackets fraction numerator 4 straight x to the power of 4 over denominator 4 end fraction minus fraction numerator 5 straight x cubed over denominator 3 end fraction plus fraction numerator 6 straight x squared over denominator 2 end fraction plus 9 straight x close square brackets subscript 1 superscript 2 space equals space open square brackets straight x to the power of 4 minus 5 over 3 straight x cubed plus 3 straight x squared plus 9 straight x close square brackets subscript 1 superscript 2 equals space open parentheses 16 minus 40 over 3 plus 12 plus 18 close parentheses space minus space open parentheses 1 minus 5 over 3 plus 3 plus 9 close parentheses space equals space 32 2 over 3 minus 11 1 third space equals space 21 1 third$

90 Views

48.

Evaluate $integral subscript 0 superscript 1 fraction numerator dx over denominator square root of 1 plus straight x end root minus square root of straight x end fraction.$