GATE CSE
First time here? Checkout the FAQ!
x
0 votes
67 views
$\int_{- \pi }^{\pi} t^{2} \sin t \ dt$
asked in Calculus by Active (2.3k points)   | 67 views
Use the rule $\int_{-a}^{a} f(x)$ = {0, if f(-x)=-f(x); 2$\int_{0}^{a} f(x)$ if f(-x)=f(x)}

1 Answer

+3 votes
Best answer

See the basic property :

-a∫ a  f(x)  dx =   0 , f(x) is odd

                  =  2 0a f(x) dx

So here :

The function f(x)  =  x2 sinx  is odd as we know product of odd function and even function is odd function only..

Therefore the given integral value =  0.

Hence  0 is correct answer.. 

answered by Veteran (65k points)  
selected by

Related questions

Top Users Feb 2017
  1. Arjun

    5288 Points

  2. Bikram

    4230 Points

  3. Habibkhan

    3952 Points

  4. Aboveallplayer

    3086 Points

  5. Debashish Deka

    2378 Points

  6. sriv_shubham

    2308 Points

  7. Smriti012

    2236 Points

  8. Arnabi

    2008 Points

  9. mcjoshi

    1690 Points

  10. sh!va

    1684 Points

Monthly Topper: Rs. 500 gift card

20,860 questions
26,010 answers
59,673 comments
22,113 users