Question

Characterize the below integrals (definite or indefinite) and solve the integrals: a. S(-10x5 + 3x2 - 5x)dx b. S(-8VxG)dx c. 5 (3x6 - 11) dx d. S(12e* - 9 sin x + 5x-2)dx e. ; (*********=-)dx

Answer 1

Note © Defirate integral Given thin the oliférate integal of f is =c es constant . function f of a real Lauable x and an interval [a,b] of the real line, f@dx ¿ is a constant ® the value of definate integral cuull always be Indefirate Integral indefinate integral of feniken fajcie @ In defirate integral doesnot bane limits of integral and the inteziel gernes a function of a tilt is asked to characterize the integrals given into depirate of indefinate integral and to solue The f is to F(x) them

Note Sanabe n+ * None of the integrals gernen in the question has limits of integration. Thesiefone all the given integrals (9,b,c,d ande) are indefinate integrals Sandbe = gnt! + C. ,n7-1 $t che = injal to integration · Szinga)ele = -cos) +C 10x 3 + 3x² - 5x) dx -S6102°437?_5x) = -roſzędx safz'du-s/36 > C-constant of addox ear tc 511 it - 10 x 5+1 2+) +3.2 -5.X 2+1 F C 1+1 6 3 = 10 x + 3 x 25 x + c 6 3

- w17 a te x² - 2 x ² + c S610x + 3x² 52 )one = as x + x ² - 9 2 + c St 8 + 2) ok -88 Cox S) te che --8 Sa & che = -85 x x + c 5-8.2 3+] 2 NOT =-8.x & C lottare 5/2 5/2+C -16 5 x 563976) oke --16** C Il & su de-11 5 1 2 dx X, -) dx = 5. xt -11 Inlalte 6 7 Health 5.27-11n 1x1 + c = 42

(8 x 8 - 14 Joze 7 5x - 11. Inlal+C 42 ?_q8nm) + 5e? Jak lage dlx - 9 Savingsche be + osoczole +C -2+1 =12.0^-9x.cos (X) +5.2 -2+1 = 12e?+9 C08 ()-52''to Scae? 9.5x2)+572)tx = lac 790sx)- 57'+01 S6 x 42 - 4x-1 Jor = {(6 x ² + x -+- 22 h - 65 2" dx + {xdx - Srce - S x + 5 6.x 5 2 x + x - 4X-) Jobe 2 - 4X-Inlal +C a +2% -4%-In)x1+C