solve the equation for al solutiins in intewal [o,2 round answers to s places 8 Sinlzt)-2 sinlt)=0

Q: Find both first partlal deriva N = sinh(8x + 13y)

A: The function given is z= sinh(8x+13y) and we know that derivative of sinhx is coshx

Q: 3) | (1– cos² 2t) dt (Trigonometric int.)

A: ∫0π(1-cos22t)32dt

Q: Evaluate the indefinite integral ds= %3D

A:

Q: Find the area between the curves y = 4 cos(6x),    y = 4 sin(12x),    x = 0,    x = π/12

A: Given,

Q: Find hale reange Sine series Ex 2 (odd fourier sseries) For the function

A: Given function is: f(x)=x, 0<x<π2π2, π2<x<π Here, L=π f(x)=∑n=1∞bnsin(nx), where…

Q: Evaluate the integration 2.5 o cos(x) with h=0.5 by using 3/8 Simpson Rule. Write your answer in 4…

A: The Simpson's 3/8 rule states,∫ydx=3h8y0+2y3+y6+ . . . + yn-3+3y1+y2+y4+y5+ . . . +yn-2+yn-1+ynWe…

Q: Find the value of u in the interval 30°, 90°4 in decimal degrees, if sin u = 0.27843196. Give the…

A: sin u=0.27843196⇒ u=sin-1(0.27843196) Now by using a calculator, we have…

Q: To integrate by u-substitution, which part of the integrand should you choose as u? S cos de sin² x…

A:

Q: What is the integrable form of sin-cos-sin@ de? 2 2 sinu du cosu du

A:

Q: 15. Use a suitable change of variables to determine the indefinite integral. [1²cos² (1³) sin(1³)dt

A:

Q: to tal differential of eind the the り23 function ] 2=e + tan Z= Sin 2.

A:

Q: 4. Evaluate the integral sin x cos x dx by two methods: first by letting u = sinx, and then by…

A:

Q: Write down an integral expressing the length of the curve y = cos x, 2 2

A: Apply the below formula: L=∫ab1+dydx2dx

Q: 5. Evaluate the indefinite integral. S cososin'oc (1) (3x - 2)20 dr (2) (3) S etanr sec?rdr

A:

Q: integrate sqrt(9* sin^2 (4theta*t) - 1) dt

A: we need to find ∫9sin2(4θt)-1dt Let us take  u=4θt⇒dudt= 4θ⇒dt=du4θ

Q: 4. A cannon ball is shot From the position (0,0,100) with initial velocity (100,120,40) when and…

A: Initial sped of the ball u=(0,0,100) x0=(100, 120, 40) Acceleration due to gravity g=(0,0,-32)…

Q: Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) trapezoidal rule, (4) parabolic…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: To the polar coordinates to hich integral is transformed. when converting the integral.

A:

Q: Find the area between the inner and outer ovals of r = 4(1+sine

A: I am going to solve the given problem by using some simple calculus to get the require

Q: sine da Seco co?o

A:

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: Estimate the error if cos Vt is approximated by 1 – in the integral , cos Vi dt. 4! 6!

A:

Q: 8. Find the area enclosed by 1 leaf of r=sin30

A: Let's find.

Q: What is the integral of 10pi(4-y)(sqrt(siny))dy from 0 to pi?

A: Let I=∫0π10π4-ysinydy Then, ∫0π10π4-ysiny…

Q: Evaluate the integral (1+ etane) Sec?0 de

A: The given integral is, I=∫0π41+etanθsec2θdθ Let us solve the given definite integral using the…

Q: Find the intersection area between r = 3sine and T = 2 - sine curves.

A: given, r=3sinθ  and r=2-sinθ

Q: evaluate the intregral of cos2xesin2x dx

A: topic - indefinite integral

Q: Evaluate the definite integral. ∫(lower bound=π/4)(upper bound=0)sin(4t)dt

A: Given,             ∫π40sin4tdt

Q: evaluate the integral using the methods covered in the text so far.

A:

Q: Solve part d) only Differentiate Show all work

A: d) y=-12e1x2

Q: Find the area in the first quadrant bounded by the curve Y = 4–?^2 and the axes using horizontal…

A: Consider the region bounded by the the curve and the axes in the first quadrant

Q: Determine the following indefinite integral.

A: To calculate the given integral

Q: Solve the intial- value Pioblem: y-cosx-Sinx ty 040S y)=0. di using Milne's method

A:

Q: #z. {valvate the following definite intgrals. .3 elx 9. Cosx Sinx lx

A: We have to solve

Q: Determine the following indefinite integral.

A:

Q: Calculate the area between the curves ² = 16 sin 20 and ²: = 16 cos 20 .Show by drawing

A: Given: The curves r2=16cos2θ , r2=16sin2θ To find: Area bounded by two curves  r2=16cos2θ ,…

Q: Use double integrals to find the area inside the curve  r = 3 + sin(θ).

A: Find the area enclosed by the curve r = 3+sin θ , using double integration method.

Q: Use an appropriate u-substitution to evaluate the indefinite integral 3sin (71)cos(7)dt. Use C'for…

A: Use substitutions to integration

Q: Given: J Vx sinh TV

A:

Q: 5. sin² 4y cos? 2y dy

A: Given: I=∫0π4sin2 4y cos2 2y dy  ……1

Q: 5. Find the area enclosed by the inner loop of the curve r = 1-3 sin 0

A: Area Between Functions With Integration: The interval of the inner loop of the given polar curve is…

Q: Find the indefinite integral. I sini sin³ 70 √ cos 70 de

A: Given problem :-  ∫sin3(7θ) √cos(7θ) dθ

Q: 3. Change the order of integration sin dydx. Hence, evaluate the integral. y

A: Sol ∫0π∫xπsinyydydxChange order of integration =∫0π∫0ysinyydxdy

Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

A:

Q: What is the integrable form of sin 0 sin-cos-sine d@? 2 2 u² – 1 du 1– u² du 2 | cosu du -2 | sinu…

A:

Q: Evaluate the integral. 8 sinh O 8 sinh c sin sinh 즐

A:

Q: 10. Evaluate the indefinite integra a) S sinxecosx dx b) Seda 1+vx

A:

Q: Make a substitution to express the integrand as arational function and then evaluate the integral.…

A: To find the integral: ∫sinxcos2x-3cosxdx Let substitute t=cosx Differentiating both sides,…

Q: Solve the integral by two grid in the y-direction and four grid in the x-direction with Trapezoidal…

A: The given integral is: ∫45∫23xcosydydx Here  x0=4, x1=5y0=2, y1=3fx,y=xcosy By Trapezoidal rule,…