(1 point) For each of the following integrals, select an integration technique that could be used...
208 and 212 please ❤️ Evaluate the following integrals, which have irreducible quadratic factors. 207. 2 -dx (x – 4) (x2 + 2x + 6) s . x2 208. -dx x3 – x2 + 4x - 4 209. x3 + 6x2 + 3x + 6 -dx x3 + 2x2 _ - 210. -dx (x - 1)(x2 + 2x + 2) Use the method of partial fractions to evaluate the following integrals. 3x + 4 211. -dx (x2 + 4) (3...
Integration by substitution 1. Find each of the following indefinite integrals using integration by substitution: dz (a) / (xºcos(x4) ) do (c) / (sin(2) cromka) die (e) / (24) do (a) / (2.eller) die (0) / (zlog.cz) Integration by parts 2. Find each of the following indefinite integrals using integration by parts: (a) / (+cos(x)) dx (c) / (vVy + 1) dy (e) / (sin”(w) ) at (8) / (sin(o) cos(0) ) da (b) / (x2=+) di (a) / (x2108_(2))...
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 -...
5. Use a substitution and an integration by parts to find each of the following indef- inite integrals: (b) | (cos(a) sin(a) esas) de (a) / ( (32 – 7) sin(5x + 2)) de (c) / (e* cos(e=)) dt (d) dr 6. Spot the error in the following calculation: S() will use integration by parts with 1 We wish to compute dr. For this dv du 1 dar = 1. This gives us dr by parts we find dr =...
Question 5 (0.5 points) Use an integration by parts to find which of the following integrals is equivalent to In(22 - 2 + 2)dx In(x2 – 3+2)+ | J 2x2 – 3 2 - 2 + 2 zin(c? – + 2) - Sen todo xln(x2 – 2 +2)+%22277, da xln(x² – 2+2) + 2x2 – 3 1 x² – x+2
could u explain step by step For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral. a. fax – 3y die X = b. - x2 V7x2 +5 dx X = c. · S xV7x? – 28 7x? - 28x + 21 dx X = d. - dx - 119 - 5x2 + 50x X =
(a) i) For ∫(4x−4)(2x^2-4x+2)^4 dx (upper boundry =1, lower =0) Make the substitution u=2x^2−4x+2, and write the integrand as a function of u, ∫(4x−4)(2x^2−4x+2)^4 dx =∫ and hence solve the integral as a function of u, and then find the exact value of the definite integral. ii) Make the substitution u=e^(3x)/6, and write the integrand as a function of u. ∫ e^(3x)dx/36+e^(6x)=∫ Hence solve the integral as a function of u, including a constant of integration c, and then write...
Use partial fractions, completing the square, and/or integration tables to find the following definite integrals (make it clear which method you use) (a) 18 dx 12 - 49 (b) 1 20 dx 22 - 72 10 | | (c) 6 dx 12 - 4 - 5
(1 point) Calculate the integral below by partial fractions and by using the indicated substitution. Be sure that you can show how the results you obtain are the same. 1. 2x - dx 1 x² – 64 +C. First, rewrite this with partial fractions: I ZX64 dx = | dx + dx = (Note that you should not include the +C in your entered answer, as it has been provided at the end of the expression.) Next, use the substitution...
Using trigonometric identities and substitution, evaluate the following integrals: 1. S sin5 x dx 2. Shamrzdx 3. S V4 – 9x2dx 4. Sýsin? x dx 5. S 1 dx x2 +81