Search for: Let f:(0,∞)→R and F(x)=∫0x f(x)dt. If Fx2=x2(1+x) then f4 is equal to Let f:(0,∞)→R and F(x)=∫0x f(x)dt. If Fx2=x2(1+x) then f4 is equal to A5/4B7C4D2 Fill Out the Form for Expert Academic Guidance!l Grade ---Class 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12 Target Exam JEENEETCBSE +91 Preferred time slot for the call ---9 am10 am11 am12 pm1 pm2 pm3 pm4 pm5 pm6 pm7 pm8pm9 pm10pm Please indicate your interest Live ClassesBooksTest SeriesSelf Learning Language ---EnglishHindiMarathiTamilTeluguMalayalam Are you a Sri Chaitanya student? NoYes Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:Given, Fx2=x2(1+x)⇒∫0x2 f(t)dt=x2(1+x)On differentiating both sides w.r.t. r, we get 2xfx2=2x+3x2⇒fx2=1+3x2⇒f22=1+32(2)=4⇒f(4)=4 Related content CBSE Class 12 English Lost Spring MCQ with Answers Heron’s Formula Class 9 Worksheet Maths Chapter 12 CBSE Class 12 English The Last Lesson MCQ with Answers Was NEET 2024 Paper Leaked? Check NTA Official Press Release CBSE Class 10 English Chapter 1 Worksheets -A Letter to God Disaster Management Project for Class 9 ICSE ISC Topper List 2024, Check ISC Class 12 Topper List for Science, Commerce, Arts Class 9 Science MCQ Chapter 12 Sound CBSE Class 12 English MCQ with Answers (Flamingo & Vistas) CBSE Class 7 Science MCQ Questions with Answers