If R = {(x, y) : 0 ≤ x ≤ 1,0 ≤ y ≤ 1}, then find (²+1) +2 0 1 arctan O 2√2 3 0 √2 3 O √2 3 (√³/₂2) (+) arctan arctan -arctan 3 (2) dA

Q: 2.2 y = (x³ − 1)(x² − 2x + 1) using the product rule. √1 + tan² x 2.3 y= sec² x

A: solution of the given question is like aS:

Q: Q4: A) Find one of the following: 1) If x=0-sin(0) and y=1-cos(0) find the length of the curve…

A: If  and , then to find the length of the curve between .Note: Since the student has posted multiple…

Q: 6. Identify the proper trigonometric substitution and then solve the integral 1 dx (x² + 1)²

A:

Q: a) Use the definition of the hyperbolic functions to prove that 2cosh?(x)–1=cosh(2x). 1%3D

A:

Q: 5. Evaluate: 34 l vo dx dx. √9-16x2 0

A: To find the value of given integral.

Q: P8: sin x cos x (2 sin x – 1)(sin x + 1)

A:

Q: Determine the order, degree, unknown function, and the independent variable of the DE 2x + 3x – 5x =…

A: in the first problem  order = 3 degree =1 unknown function =x(t) unknown variable = x independent…

Q: 6. Evaluate: secº (1/x) tan³ (1/x) dx x² | se

A: This question can be solved using integration by substitution.

Q: Prove for a > 0:

A: ∫1x2+a2dx=xx2+a2-∫ -4x2x2+a3dx=xx2+a2+18a324arctanxa-sin4arctanxaAdd a constant to the…

Q: 3) fe-2x sin 2x dx 4) J√1 + cos 4x dx

A:

Q: d x 2. 1+xVI-(Tanin)

A:

Q: 2 a. (1+5 ln x)³ dx fa+ b. (1+3 tan x)² sec? x dx 2x + 5 dx Vr – 3 2x3 – 5x? + 9x – 4 C. - d. dx x²…

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: If = {(x, y) | 16 ≤ x² + y² ≤ 49} then: 11.000 = [ co cos (x² + y²) dA

A:

Q: dx cot 3x sin 3x -1/3 sec 3x + C

A: ∫dxcot(3x).sin(3x)=∫dxcos(3x)sin(3x).sin(3x)

Q: b) Prove that, S∞ (@3x+1)² dx e2x 2π 9√3

A: Let we get, Let We get, This implies, This implies

Q: 3. V4- (x – 3)²dx.

A:

Q: = (b) ſ sin (7(x – 2y)²) dA, where T is the triangle bounded by x – 2y T 1, y = −3x and 5y = -x.

A:

Q: Express the following in the form r(cos 0 + i sin 0), - < 0 ≤ π: (1 - i)(√3+ i) (1 + i)(√3-i)

A:

Q: A sketch of y = sin x° for-360 ≤ x ≤ 360 is shown.

A: Step 1: As we know π= 180⁰So 360 can be written as 360⁰=2πAnd -360°= -2π That is X lies between -2π…

Q: S ii) Show the DE is not exact (2y²+3x) dx + 2xydy = 0

A: Solution :

Q: 3) Suppose I want to use a "u" substitution to find sec² (9x + 4)dx. What should I choose for u? O…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: ¸¸ S'√ 16–16 x² d x = · (a) 16 π (b) π square unit. ©2π (d) 4π

A:

Q: a) 2(sin x)² - 1 = 0 [0,2π]

A: a) 2(sin⁡x)2−1=0[0,2π]