Use trig identities to rewrite the integral then integrate. 1. 2. 3. 4. 5. 6. tan(r)dr tan(r)dr (sinz + sinz + tan2)/sec2rda Sin.TS2nT (sin(2x)/cosrdr (sin(2))/1+cos2rda (cos(x) + sin(2))/sinrdr tan(r)dr tan(r)dr (sinz + sinz + tan2)/sec2rda Sin.TS2nT (sin(2x)/cosrdr (sin(2))/1+cos2rda (cos(x) + sin(2))/sinrdr
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:
QUESTION 18 Use the substitution z = tan(x/2) to evaluate the integral / 3-cos e de ОА. tan-1 ( ✓2 tan 2 --()) +C OB. tan tan +C V2 OC V2 tan 2 Etan () )+c 2 OD. 1 tan tan +C 2 OE. tan V2 tan +C 2
evaluate the following integral sec/ tan / vi+secl de
For r = e on the interval 0 <O< 1, find a definite integral that represents the arc length. Select the correct answer below: O 546 4Ꮄ dᎾ I'avas V2.de I 12 de
Evaluate the following integral in cylindrical coordinates. z T 4 4 dz r dr de 00-4 -4 4 T 4 4 SSS dz r dr do = (Type an exact answer, using a as needed.) 00-4
(3) Evaluate the indefinite integral. tan(t) + cos2 () de Con)
cos(()dr - (r sin(O) - e)de = 0, r(0) = 1 (make r the subject of the formula)
2. Since it is difficult to evaluate the integral dr exactly, we will approximate it using Maclaurin polynomials (a) Determine P4(x), the 4th degree Maclaurin polynomial of the integrand e". (b) Obtain an upper bound on the error in the integrand for r in the range 0-x 1/2, when the integrand is approximated by Pi(x). (c) Find an approximation to the original integral by integrating P4(r (d) Obtain an upper bound on the error in the integration in (c) (e)...
Evaluate the integral. IP In(r) dr