1. Evaluate the following definite integral using the substitution formula: LI 4 cos(x) sin(x)dr.
Use the substitution formula to evaluate the integral. 1/2 COS X s dx (5+5 sin x) 0 3 OA 1000 OB 3 200 OC. 3 200 OD. 12 125
Tutorial Exercise Evaluate the integral using the substitution rule. sin(x) 1/3 1* dx cos(x) Step 1 of 4 To integrate using substitution, choose u to be some function in the integrand whose derivative (or some constant multiple of whose derivative) is a factor of the integrand. Rewriting a quotient as a product can help to identify u and its derivative. 70/3 1." sin(x) dx = L" (cos(x) since) dx cos?(X) Notice that do (cos(x)) = and this derivative is a...
4. Use an appropriate substitution to evaluate the following integral: 3/4 cos(V1 – x (1 – x dx 0
dr J0 3. Let a be a positive constant such that a 1. Evaluate the definite integral using the technique in complex analysis, -C 27 dar I 1+a2 2a cos(1) Jo (a) State a precise version of Beu 4. dr J0 3. Let a be a positive constant such that a 1. Evaluate the definite integral using the technique in complex analysis, -C 27 dar I 1+a2 2a cos(1) Jo (a) State a precise version of Beu 4.
Problem 4 A definite integral I is given as .b I=| f(x) dr a=0 b=2 f(x) = e-r' ; ; ; Evaluate the integral using the three-point Gaussian quadrature method Solution: Problem 4 A definite integral I is given as .b I=| f(x) dr a=0 b=2 f(x) = e-r' ; ; ; Evaluate the integral using the three-point Gaussian quadrature method Solution:
#2 #3 #4 please snf thank you :) Evaluate the following anti derivatives (Indefinite integral) 1)「(2x3-5x + 7)dr 3 x ax Evaluate the following definite integrals: 01 2Sec2xdc Evaluate the following anti derivatives (Indefinite integral) 1)「(2x3-5x + 7)dr 3 x ax Evaluate the following definite integrals: 01 2Sec2xdc
Evaluate the definite integral two ways: first by a V -substitution in the definite integral and then by a V -substitution in the corresponding indefinite integral. = Enter the exact answer. In2 Missing Plug-in J-In2 et + a dx =
(a) Evaluate the double integral 4. (sin cos y) dy dr. Hint: You may need the formula for integration by parts (b) Show that 4r+6ry>0 for all (r,y) ER-(x,y): 1S2,-2Sysi) Use a double integral to compute the volume of the solid that lies under the graph of the function 4+6ry and above the rectangle R in the ry-plane. e) Consider the integral tan(r) log a dyd. (i) Make a neat, labelled sketch of the region R in the ry-plane over...
5. Evaluate each definite integral. 5.2 dx 2.22 [5] /2 [5] (b) [ COS C sin? C dx 1/4
3. Evaluate dr a. Start with the substitution ue and note that u2 =e2, This should lead to the integral du. b. Next use a trig. substitution u (You will end up with a sin 20. To convert back to u and then x you can use sin(20) 2 sin @ cos .) 3. Evaluate dr a. Start with the substitution ue and note that u2 =e2, This should lead to the integral du. b. Next use a trig. substitution...