11. uf /*s(a)dx = 4 and 5* $(2)dx = 5, fina [°s(dr. 12. Find ſº va=2ds. (Hint: use geometry.) 13. Compute: 'Vole? + x'")dls. 14. Find /(2x + 3) 4x2 + 12xdv.
1 (a) Evaluate the integral sz? dx. (32-7) 5 2 7 (b)if s f(x)dx = 3 and 5 f(x)dt = 4, find S f(x)dr. 5
5. (4pts each)Evaluate the following integrals. s sins (1) cos (1) dx a. dx b. sz * (ln(x))?
(1) 5 - Yps Sp de - dx to find a second solution of the DE 3. Use the formula ya = yı 9 +2+y = 0, V1 = ce* 4. Find the general solution of each DE.
Use the properties of the definite integral in your solutions. 1. Suppose that [*r(e)dx = 5, [° f(a)dx = -3, [*9(a)dx = -1, and ſº o(e)dx = 2. Evaluate Jo each of the following definite integrals. (a) %* ((e)+ 9(e) de (b) [" (F(*) + 9(a) do (e) ſ (sca) – ola) de (a) " (45(e) – 39(a) de
1. Solve the following DE: dy 6 y = 3x3 dx x
1. Calculate the definite integral 1 (229-33 +5) de (a) Find an antiderivative F(x)= (b) Evaluate F(2) F(2) = (c) Evaluate F(1) F(1) = (d) Calculate the definite integral 3x + 5) dx = 2. Calculate the definite integral. Give exact answers. Зе -Te du (a) Find an antiderivative F(*) = (b) Evaluate F(0) F(0) (c) Evaluate F(-1) F(-1) = (d) Calculate the definite integral.
If f is continuous and 6". 16 f(x) dx = 12, find Lox xf(x2) dx.
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
6. Find the general indefinite integral: J (u + 4)(2u +1)du I a. (3x dx conto de ton of b. [VF (82 +31 + 2)dx cinco T() = f(x) d. Sx dx (a=-1) sin x-e' +2 de 188