CBSE Class 12 Sample Paper for 2019 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 7

Find: β« (x 2 Β + sin 2 β‘x) sec 2 β‘x / (1 + x 2 ) dx

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Question 7 Find: β«1β((π₯^2 + sin^2β‘π₯ ) sec^2β‘π₯)/(1 + π₯^2 ) dx β«1β((π₯^2 + sin^2β‘π₯ ) sec^2β‘π₯)/(1 + π₯^2 ) dx = β«1β((π₯^2 + sin^2β‘π₯ )(1/cos^2β‘π₯ ) )/(1 + π₯^2 ) dx = β«1β((π₯^2 + sin^2β‘π₯ ) )/((1 + π₯^2 ) cos^2β‘π₯ ) dx Writing sin2 x = 1 β cos2 x = β«1β((π₯^2 + 1 β cos^2β‘π₯ ) )/((1 + π₯^2 ) cos^2β‘π₯ ) dx = β«1β((1 + π₯^2 ) β cos^2β‘π₯ )/((1 + π₯^2 ) cos^2β‘π₯ ) dx = β«1β((1 + π₯^2 ) )/((1 + π₯^2 ) cos^2β‘π₯ ) dx β β«1β(cos^2β‘π₯ )/((1 + π₯^2 ) cos^2β‘π₯ ) dx = β«1β1/cos^2β‘π₯ dx β β«1β(1 )/((1 + π₯^2 ) ) dx = β«1βγπ ππγ^2β‘π₯ dx β β«1β(1 )/((1 + π₯^2 ) ) dx = πππ πβγπππγ^(βπ) π + C