5.6 WS answer key

-(q -x)oiKI’I. t1xH4--x2. [-2212. f’()4(x÷l)________.LV33 •_LH, —-c)(,-3 q5. f(x)2-, [1,3]l- J—.-cosxj111-ç_!—\• ,,,XoLYcavj3. f(x)=sinx, [0,ir]-- .if3L4i‘11 34z-L. /3]Lesson 5.6: The Mean Value Eheorem and Fundamental Theorem of Calculus Part 23x’hitcrval for which the function equals its average value.For questions 1—6, Find the average value of the function over the given interval and aH values of x in the33—L x313-i.f--.3’(3 3Tj / L1av_L...s:’aJ x 71 ‘‘r16, f(x)=x2, 1,4]LJQ\)05 )r‘ITcoSXJ(I’C0SX4. 1(x) cosx, [0, /2J- j_•3-2 (1,3]I-..I_(LI)i•.(I(uiEE3J_. Lj , ‘If*-S3(L÷Llx)(3i_S 31t4

a. se Part of the Fundamental Theorem of Calculus to find F’(x)h. Cheek the result in vart (a) by first integrating and then differentiatinr.200 -between i = seconds and t 4 seconds?- ‘13 7-s(3x7. F(x) —4)dtS. F(x)= [(sin2fl/ta. Use Part 2 of the Fundamental Theorem of Calculus to find F’(x)b. Check the result in part (a) by first integrating and then differentiating. yi..I9, iLfsin(t2)dt 10. LJedt=11. Jlntdt 12. frsectdt=X13. The area of an oil spill is increasing at a rate of25t ft2s. t seconds after the spill. How much oil spilleddxFor questions 9-12, use part 2 of the Fundamental Theorem of Calculus to find the derivatives.F”(x’ fsrx)5--—-coucj -*co1.i. —CoSX+U