Evaluate the double integral 10 π/4 Sketch the region R. 61" R f(r, 0) dA. e) da. sin(0) cos(0) dr de л/2

Q: 4] [2M] Evaluate the iterated integral o So V sin(x2 + y? )dx dy by converting to polar coordinates.

A:

Q: 06. Evmlete the integral 7sin (a)+ 7sin(2)tan? (x) de secz (x)

A: Integrated by substitutions

Q: 8. Evaluate the integral. 2 2 (a) S(4x°. 3x + 2x)dx - 1 4 4+6u (b) S(ou)du Vu 1

A: Using rules of integration & formulae of integration.

Q: Find for x³+y³ = 2. -4x O O (E) None of these ○ 3x² + 3y² = 0 2x *(*_*) O

A: Note:- As per the company guidelines we can solve first question. I hope that the given solution…

Q: Evaluate the following integrals: 2. Inx de sin 3x 3. dx 1-cos 3x 4. S 32* dx 5. S(e* + 1)°e*dx 6.…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: a) Find the area under the curve Y = sinx and the x-axis on the interval [0, 4л] in the figure 1.…

A:

Q: 5. S 6. S 7. S dx xintx sec²ydy tan ¹5 y (x³-5x)dx VX

A:

Q: 5. Evaluate triple integral Szr? sin e dz dr d0.

A: We know that,∫sinxdx=-cosx∫xndx=xn+1n+1The given integral…

Q: Find the area inside both r = 2 sin(20), r = 2 cos 0

A:

Q: 2t : Evaluate the integral [ de 0 3+ cos(0)

A:

Q: Show that x2+4x+17 is O(x3) but that x3 is not O(x2+4x+17).

A:

Q: 1. Find y' a) y= X fanx In3 b) y= 3 <) y = (cos@)r2 %3D

A: Since you have asked multiple questions, hence we are solving the first question for you. If you…

Q: PCx g) - Sin (zy)- Cosx'+x*y? %3D find d'f df dye' de dy

A: Given function is  f(x,y) = sin(x,y) - cosx^2 + x^2y^2

Q: Y Evaluate the following integrals: 1) tan(3x +5) dx evs -1 2) dx 3) [Vx² -x' dx 4) sin(tan 0) sec 0…

A:

Q: 12. Find the area of the region shared by r = 1+ cos 0 and r = 1 – cos 0.

A: The given graphs are r=1+cosθ and r=1-cosθ We have to find the area of the region bounded by the…

Q: Evaluate the integral J dæ using trig substitution. 22-9 O 3 sec 0 O 1 v 2-9 +C O cos e +C

A: Consider the given integral: ∫1x2x2-9dx Substitute x=3secu Then, dx=3secutanudu Hence integral…

Q: a) Evaluate the following integrals i) S(x + 1)/2x + x2dx.

A:

Q: By using polar coordinates, evaluate the double integral -y²dx dy x² + y² over the region in the…

A: Answer is given using polar coordinates.

Q: 1:25 < Back Pulse From 28.6: Inverse Trigonometric Forms 26) Integrate: S 4x dx 1+x4 27) Integrate…

A: ( If you have any questions related to this problem please feel free to ask me).

Q: 4) Find the area of the region enclosed by the curves y = sin(x), y = cos (x), X = 0 and x = 2π 5)…

A:

Q: dx i- xIn x cox + sin x dx. cos x- sin x i.

A: (i) The given integral is ∫1x ln x dx. Let u=ln x. Then du=1xdx. Apply the substitutions and…

Q: Q5/ Use double integration in Polar coordinates to find the shaded area in figure (the area inside…

A: The area is A=2∫π6π4∫2 cosθ2 sin2θr dr dθ We now evaluate this: A=2∫π6π4∫2 cosθ2 sin2θr dr…

Q: Given SV-x* + 4x + 5 dx. Using trigonometric substitution, what is the integral form in terms of 8?…

A: Trigonometric identities: sin2θ+cos2θ=1cos2θ=1+cos2θ2 If an expression is x2+bx, then we need to add…

Q: if  x²v+sin(xu)-yv²+u³v=1 x²u-2yv=1 ، cos(xu)+yv=5  ,find dy/dx

A: