6.a. Let us first write the integrand in exponential form.
6. Find the general indefinite integral: J (u + 4)(2u +1)du I a. (3x dx conto...
(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.
(1 point) Find the general indefinite integral S sin 2x dx. cOS X Answer.
1. Evaluate the indefinite integral sen (2x) – 7 cos(9x) – sec°(3x) dx = 2. Evaluate the indefinite integral | cor(3x) – sec(x) tant(x) + 9 tan(2x) dx = 3. Calculate the indefinite integral using the substitution rule | sec?0 tan*o do =
1- 2- Tutorial Exercise Evaluate the indefinite integral. Jerez 42 + ex dx Step 1 We must decide what to choose for u. If u = f(x), then du = f'(x) dx, and so it is helpful to look for some expression in Jerez 42 + ex dx for which the derivative is also present. We see that 42 + ex is part of this integral, and the derivative of 42 + ex is ex et which is also present....
(3 points) Find the general indefinite integral. (Use C for the constant of integration.) [(4 sin(x) + 2 - x) dx
(1 point) Evaluate the indefinite integral. dx = Inabs((1/3)(x^3)+x^2-3x) (x - 1)(x + 3)
find the indefinite integral and check the result by differentiation Analytic Geometry & Calculus II, Final Examination Part I, Spring costx)swLx) b) J sin 2x cos 2x dx 2 (-cos (4)(Hx) check. (x-5)=2 xs_6x-20 dx Analytic Geometry & Calculus II, Final Examination Part I, Spring costx)swLx) b) J sin 2x cos 2x dx 2 (-cos (4)(Hx) check. (x-5)=2 xs_6x-20 dx
10. (16) Find each indefinite integral using u-substitution: a. x?(1–2x")*dx b. ſxcos(x2 – 1) dx
6. (10 points) Find the general indefinite integral showing all work to justify your result sin(2x) 7 3 + - 5*) dx 1+x2 s sinx sin x
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integral dy dx into an integral over G, and evaluate both integrals a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then...