a2f, a2f Q1: A- Show that + əy? ду? = 0, where f(x, y) = In(x² + y²) + tan-() %3D B- Evaluate the integral 나c dz dy dx 1-x² 3-x-y 1-x2.

Q: integral by part x² dx

A: Given that  The integral is

Q: Use u-substitution to find the definite integral |4xe -3x+7 dx . Please clearly show all -k.

A: By u - substitutions

Q: Find div F and curl F if F(x, y, z) = x³i - 10j+yzk. div F= curl F=

A:

Q: 2x2 dv, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0,…

A:

Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: 1 Circles

A: To Setup: Integrals for the area of the shaded region in both figures.

Q: I) S dx/ (x² + 4x + 3) find integral

A:

Q: sin z dz, C (z+1)7 tan (z/2) ii) J. dz C Z-T/2

A: To Solve the above integral we use Cauchy Integral Formula.Given in Second Step.

Q: Find div F and curl F if F(x, y, z)=xi - 10j+yzk. div F= curl F=

A:

Q: Find domain and vange f (2y)- し、 (x'+ゴ) ) fCz, y) = Sin" (y-z) Ž (3,y)- tan

A: According to the question,  We need to specify the domain and range of the given function: (A) f(x,…

Q: f(x,y) af ?x af ду = af ду X 2x² + 8y² f(x, y) = tan af ?x (5)

A:

Q: For the function f(x,y) = sin (3x − 7y), find of of dy of af and ?x ду

A:

Q: sinx

A:

Q: x2-3x-28 dx is a minumum. x2+1 (a) Find the interval [a, b] such that Ja x2-3x-28 x²+1 (b) Find the…

A:

Q: Which of the following pair of functions is linearly independent? (a) e3*, e(x-3) (b) 4, sin?x +…

A:

Q: 2(x + y)i + sin(y) 3. Find the line integral of Faround the perimeter of the rectangle with corners…

A:

Q: TT 4 3. f(1 + sinx) dx + f(1 + sinx) dx 0 TU 4

A:

Q: af If f(x,y) = sin-(4x³y?) then dx 12x?y? 1-(4x³y²)² O a. b. 1 4x³y²/(4x³y?)² – 1 c. 12x²y² 4x³y?…

A:

Q: Let f(x, y) = (5x – y)*. Then %3D дхду Эхдудх dx² dy

A: Partial derivatives: It is a derivative of a function of two or more variables with respect to one…

Q: 2ху dx + (x + у) dy Jc C: boundary of the region lying between the graphs of y = 0 and y = 1 – x2

A: Given: ∫C2xy dx+(x+y)dy y=0 and y=1-x2

Q: Let y = xbex (where b is a real number). Determine y'.   Let y = (3x + 6)/(6x + 12). Determine y'.

A: given y=xbex to find the derivative y' use the product rule uv'=uv'+vu' therefore,…

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: 3x + 2 dæ, Hint: Remember that 4 = 4 + . = +. A+B 4. b) Integrate %3D

A:

Q: 1 point) Calculate the integral: 1 dx = (x + 8)(x + 4)

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.