Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

 If    for    a    continuous    function   f(x),     \int_{-\pi }^{t}\left ( f\left ( x \right )+x \right )dx= \pi ^{2}-t^{2}

for all  t\geqslant -\pi then f\left ( -\frac{\pi }{3} \right ) is equal to:

  • Option 1)

    \pi

  • Option 2)

    \frac{\pi }{2}

  • Option 3)

    \frac{\pi }{3}

  • Option 4)

    \frac{\pi }{6}

 

Answers (1)

As learnt in concept

NEWTON LEIBNITZ THEOREM -

\frac {d}{dt}\left ( \int_{f(t)}^{\phi (t))}F(x)dx \right )=F(\phi(t))\phi^{'}(t)-F(f(t))f^{'}(t)

-

 

 \int_{-\pi}^{t}(f(x)+x) dx\:=\: \pi^2 -t^2

Differentiating by leibnitz rule

(f(t)+t) \times 1 -0\:=\: -2t

f(t)\:=\: -3t

f(\frac{-\pi}{3})\:=\: -3 \times \frac{-\pi}{3} =\pi


Option 1)

\pi

Correct

Option 2)

\frac{\pi }{2}

Incorrect

Option 3)

\frac{\pi }{3}

Incorrect

Option 4)

\frac{\pi }{6}

Incorrect

Posted by

Vakul

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025 chemistry needs conceptual understanding; 5 tips to score high
anam-khan

JEE Main 2025 exam city intimation slip for session 1 soon; paper pattern, exams from January 22
anam-khan

JEE Main Maths 2025: Five tips to score high marks in ‘toughest’ subject; most important chapters

Latest Question