so, u should be 2x+3.
solve using Trigonometric Substitution iz= Se«»/1+e2x dx
3. Use the u-substitution method to calculate the following indefinite Integrals a. S(x2 - 4)2x dx u= b. Sx?e**dx u= dur C. Sx sinx? dx U= dus
Decide on what substitution to use, and then evaluate the given integral using a substitution. HINT See the FAQ a the end of the section for advice on deciding on u, and the examples for the mechanics of doing the substitution.] (4 10.2e344 dx +3.000024034x-4x + Decide on what substitution to use, and then evaluate the given integral using a substitution. HINT See the FAQ a the end of the section for advice on deciding on u, and the examples...
Solve the initial value problem 2yy' + 2 = y2 + 2x with y(0) = 4. To solve this, we should use the substitution u = With this substitution, y = y' = Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. The solution to the original initial value problem is described by the following equation in x, y.
Use reduction of order y'' + 7y' - 18y = ex + e2x
(3 points) Consider the indefinite integral X – 3 (3x - 2)2 dx. The substitution u = 3x – 2 transforms the integral into: | du (This answer must be a function of u.) Note: You are not asked to evaluate the integral.
Integrate ve 2e22 (e22 da using U-substitution: 50 U = du dx Substitution gives du Integration yields The final answer is
Make a u-substitution and integrate from u(a) to u(b). x/20 5 tan 5x sec25x dx 15 x/20 5 tan 5x sec 25x dx = [] (Simplify your answer.) -115
1) Determine whether the integral is convergent or divergent. ? 71 ex e2x + 3 dx 0 It reads the intergral is infinity on top and 0 on bottom. It is 71* e^x/e^2x+ 3 convergentdivergent If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) 2) Determine whether the integral is convergent or divergent. ? 3 sin2? d? 0 (infintiy on top, ? = alpha) convergentdivergent If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)...
Math 2510 Take Home 3 2. Fubini? Consider the function al Use the substitution u-xy (treating x as a constantl to evaluate x-y dy b) By comparing 1 (a) with 2 (a) you should be able to predict the value of Xydy dx (x+y) c) Do these results violate Fubini's Theaorem? Explain! Page 3 of 8