D) 0 [13] Rewrite r dz dr de in spherical coordinates. J/4 0 Jo Jx/4 J
D) 0 [13] Rewrite r dz dr de in spherical coordinates. J/4 0 Jo Jx/4 J
(1) Evaluate the integral. (Hint: Substitution Rule) (2.1 + 3)(2x + 6x + 1)*der
Please include steps.
3) Consider the definite integral J rtane)de. Note that this integral cannot be evaluated with integration by substitution or by parts. a) Using appropriate subintervals, compute L4R4, M. and T. Clearly show your work by hand. b) Which of the approximations in a) are underestimates of the true value of the integral and which are overestimates? How do you know? c) Compute S, by hand, showing your work.
3) Consider the definite integral J rtane)de. Note that...
de 14) 55+ Acos e sin de 5+ 4 cos e 13) 2 - cos 15) cos 2 de 1-2k cos A + k? < 1)
Problem 13. You don't have to use the Weierstrass substitution for trigonometric integrals. Sometimes you can find a substitution that works more easily (fewer steps) than the Weierstrass. By "trigonometric integral", I mean the integral of a rational function of sine and cosine. You can use the Weierstrass substitution with integrals like SVsin(@) de, but you won't get an integrand having an "elementary" antiderivative. However, the Weierstrass substitution always yields an integral we can evaluate explicitly, whereas an ad-hoc flavor-of-the-day...
For Questions 1, 2, 3, and 4. A rear-window de-icer in a car consists of 13 resistive wires connected in parallel to a 12-volt battery. The de-icer has to be able to melt 2.1 x 10-2 kg of ice at 0°C to liquid water at 0°C in 5 minutes. Each wire is 1.3m long. Question 1 How much energy in Joules does each wire have to put out? Question 2 How much power in Watts does each wire have to...
1. Solve by making a substitution to reduce the given second order De to a first order DE. 1. x? y" + 2xy' - 1 = 0, x>0 (ans. y = Cix-1 + 2 + In x) 2. y" + y(y')} = 0 (ans. 1/3 y3 - 2c1y + C2 = 2x) 3. y'y” = 2, y(0) = 1, y'(0) = 2 (ans. y = 4/3 (x + 1)3/2 - 1/3)
A particle has a de Broglie wavelength of 2.1 x 10-1°m. Then its kinetic energy increases by a factor of 3. What is the particle's new de Broglie wavelength, assuming that relativistic effects can be ignored? Number 1.62e-10 unitsym the tolerance is +/-2%
DETAILS Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation. xdy 1 dx + y =
MY NUTES 7. DETAILS Solve the given differential equation by using an appropriate substitution. The DE is of the form dy = f(x + By + C), which is given in (5) of Section 2.5. dy dx = (x + y + 5)2