The equahon of the gruph is Hx) =Sxcosx+2 two integrals: Set up one Hnat will find the arclength of the wrue ,and the other that uill find the Surtace area rotated about the X-axif. it the curue is Do SOLVG てHに (NてEGRALS.

Q: Va2-x2 ху(х + у) dydx

A: The double integral can be calculated by calculating the integral of the function twice. First solve…

Q: ase Sabstitution metheul to sclvo + 2 Cest cosy. %3D

A:

Q: Scotx 3. csexde Csexdx

A: Note: As per company's policy we are supposed to solve only one question. So kindly repost the other…

Q: Find dz given:Za fixry}==x+2xy+4y2

A:

Q: Construct the lagsange, intexpo polynomial AL for the function y=Sin faking the points ス=0 ズ(=ー スー4

A: The given function is, y=sinπx For the given points the functions values are,when x0=1 then…

Q: 4) Evaluate 51/²₁ e¹²+¹ dydx 2x

A:

Q: PIND F'): b. FG)- 4- ax*)

A: Given: f(x) = 4-3x25 To find: f'(x)

Q: and subs. a. Sx²(x³ +5)6 dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the arclength of y = 2x² - 5 on 0 ≤ x ≤ 1

A: Given: y=2x2-5 on 0≤x≤1 To find: Arc length.

Q: 5. Consider the doubre inteya/ siacy) dy dx Af ter switching erder of integratian, lbecanes in…

A: First we will identify the region of the integration using the limits and sketch the region then we…

Q: a) [² -da rlnr b) √ JI dr √1-² arcsin x c) / 1+ Leide [" 1+424

A:

Q: Q7) Set up the integral representing the length of the curve (sint, cos² t), cos"e). - – s1s. <t< 2

A:

Q: 9. √√4-4x² Convert ₁42(4-4x² - y²)dydr into a triple integral with dV = dydzdx. C

A: Given :∫-11∫-4-4x24-4x24-4x2-y2dydx and dV=dy dz dx To convert the double integral into triple…

Q: Giren that S ) FWdx=2ondd SZ flx)dx=-7Pnd the roluç of 76Sdx Plx)dx=-77ndthe Yoluç. of

A:

Q: obtan al the real solutons af 4sinhte 4onh 42 -17 sinh3x + 4 sinhzz =0

A: Note that x=0 is a solution of 4sinh4x-17sinh3x+4sinh2x=0.

Q: ff*f*dzddy as an equivalent iterated integral in the B. Re-write the triple integral following…

A: Here firstly finding the curve using the limit then we saw that the region is the part of first…

Q: Use geometry and properties of integrals to evaluate

A: Given integral is ∫15 x-2+-x2+6x-5dx. The above integral can be written as below. ∫15…

Q: Choose a u-substitution and rewrite the integral in terms of u: 7 dx 9- 25x2 7 du 50 Vu du O -350 7…

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Q: Find the integral b) Use the subslilation

A: This question is based on Integration.

Q: Materm tvamare the inte aral:\

A: This question is based on indefinite integral.

Q: Integrate by means of substitution a) S√√4x - 7 dx =

A:

Q: b)/xvx² +9dx X+3 2. dxp (x² + 6x + 1)' +1)' d)4x -ldx x+1 dx Vx² +2x- 4 uoluste each integr

A:

Q: d) S dx 4+x6

A: Explanation of the answer is as follows

Q: Use geometry and properties of integrals to evaluate the followingdefinite integrals.

A: Given

Q: Evaluate the integral using FTC I.

A:

Q: In circle R with m/QRS = 124 and QR = 16 units find area of sector QRS. Round to the nearest…

A:

Q: Evaluate o 2x³ + 1 dx. Notice: the integrand is found between the symbols and dæ. Therefore, +1 is…

A: To evaluate:∫042x3+1dx

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.