1.) Find the definite integrals a.) sdx b.) S dx x2-4x+9 c.) ſ 4arccos xdx d.)...
4. Evaluate the definite integrals: A) |_ In xdx 1 xV1+ ln² x I dx cos x sin x a f / Inx di -d
10. (26pts) Find each of the definite integrals, indefinite integrals, and derivatives. 2 dx .22 5) / see?zda (7 - cos x) dc (d) dc sin (x2 – 4) dt (e) ["47" (3+z")" dx () /22"/+ 2 du
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
F) 3w-5 w-25 (2) Which of the following definite integrals cannot be evaluated using the Fundamental Theorem of Calculus? (This has nothing to do with being able to find an antiderivative), D) S B) sin() In(x) dx (C) x tan(x) dx A) dr dx 1+e In(x2 +1) dx sin(® dx\ (G) J V+ sin H) F) 2 dx o )u xb [(x)1-(x)ul, 3 x+1dx be evaluated using the FTOC ? C)
F) 3w-5 w-25 (2) Which of the following definite...
Q1 dx, 115 5xita dx. 2) ſ tan°4x dx . 3) 06-341 S[cos(x? 4) + 1) + xdx, 5) prove that I cscu du = -Inlcscu + cotul + c x2 + Q2 r3 dx 1) dx 2) sino cosºede , 3) /* sec°8 de , 4) * sec`e do , 4) , Port + 4 1 5) dx . 4- x2) 4 Q3 Answer A or B (graph the functions) A-Determine the area of the region enclosed by y...
9. (12 pts) Evaluate the following definite and indefinite integrals: (a) 12 dt d dx 1* 2 t Hint: Apply Part 1 of the Fundamental Theorem of Calculus and the Chain Rule. (b) /6 sin 20 de (sin2 @ + 2)2 -
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...
Suppose that f(x)dx = 9. Find the value of the following definite integrals. Complete parts (a) through (d). = (Type an exact answer, using radicals as needed.) (b) ] v3f(z)dz = dz=1 (Type (Type an exact answer, using radicals as needed.) (c) f(t)dt = (Type an exact answer, using radicals as needed.) |[-f(x)]dx = (Type an exact answer, using radicals as needed.)
4. [25 points) Solve each of the following definite and indefinite integrals. Show all of your work for full credit. For definite integrals, leave numerical answers in exact form (without rounding). Please double-check to make sure you copy the problems correctly, as minor typos could change the difficulty of these substantially. a. 1(413 – 1/3 + 1)dt b. Syndx c. S x cos(3x) dx d. S 6x sin(3x) dx e. 2y In y dy
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