GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
114 views
$\int_{0}^{\frac{\pi}{4}}( \sec 2x -\tan 2x )\ dx$
asked in Calculus by Active (2.3k points)  
edited by | 114 views
log2.
-----
please explain with steps.
Ans given as (1/2) ln 2

1 Answer

+2 votes
Best answer
$\int$sec2x = 1/2 * ln|sec2x + tan2x|

$\int$tan2x = -1/2 * ln|cos2x|

$\int_{0}^{\prod/4}$(sec2x - tan2x) = $\int_{0}^{\prod/4}$(1/2ln|sec2x + tan2x|+1/2ln|cos2x|) = $\int_{0}^{\prod/4}$(1/2ln|1+sin2x|) = 1/2ln2
answered by Boss (7.3k points)  
edited by
please check it if there is any mistake
answer given as (1/2) ln 2
∫sec2x = 1/2 * log|sec2x + tan2x|

∫tan2x = - 1/2 * log|cos2x|

these are correct
@pavan is correct . @gate u did make a mistake :)  it willbe 2 ln 2
thanks :)
yeah corrected!! thanks


Top Users Mar 2017
  1. rude

    5246 Points

  2. sh!va

    3054 Points

  3. Rahul Jain25

    2920 Points

  4. Kapil

    2732 Points

  5. Debashish Deka

    2602 Points

  6. 2018

    1574 Points

  7. Bikram

    1444 Points

  8. Vignesh Sekar

    1440 Points

  9. Akriti sood

    1424 Points

  10. Sanjay Sharma

    1128 Points

Monthly Topper: Rs. 500 gift card

21,556 questions
26,907 answers
61,268 comments
23,278 users