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Question: Answered & Verified by Expert

-π2π2sinx-xdx=, where . denotes GIF

MathematicsDefinite IntegrationTS EAMCETTS EAMCET 2021 (05 Aug Shift 1)
Options:
  • A 3(1-cos1)+sin2-sin1
  • B cos2-sin2
  • C 3(1-cos1)+cos2-sin1
  • D 0
Solution:
1256 Upvotes Verified Answer
The correct answer is: 3(1-cos1)+sin2-sin1

I=-π2π2sinx-xdx, where · denotes G.I.F.

I=-π2-1sin2+xdx+-10sin1+xdx+01sinxdx+1π2sinx-1dx

I=-cosx+2-π2-1-cosx+1-10-cosx01-cosx-11π2

I=-cos1-cos-π2+2-cos1-cos0-cos1-cos0-cosπ2-1-cos0

I=-cos1+sin2-cos1+1-cos1+1-sin1+1

I=31-cos1+sin2-sin1

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