Using polar coordinates, evaluate the integral sin(x² + y²)dA where R is the region 1 ≤ x² + y² ≤ 64.

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A: We have to solve  part 1, 2 and 3.

Q: The general solution of y" + y = sec³ x

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Q: 1. 2. dx dx sin²(x² + 2x + 1) [4 tan(3x³) - 5 csc x]

A: To find derivatives

Q: 5- prove that - for sin Ꮎ dᎾ cose Ꮎ dᎾ

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Q: 8. Find the area between y = sinx cosx and y = sinx, over the interval 0 <x<T

A: Given y=sinx cosx &amp; y=sinx between the limits x=o to x=πTo find area between two curves:

Q: . For questions and Given: A thermometer reading is 60°F at 3:00AM and a Civil Engineering student…

A: This is a problem related to differential equation. Based on the newton's law of cooling we will…

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Q: . Find the centroid of the solid generated by the area bounded by y = sin x and the lines x = 0; x =…

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Q: Homework: MML 1.1 T Line Find the slope and the y-intercept of th y=6-2x Select the correct choice…

A: Given query is to find the slope and y intercept of the line.

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: I am attaching image so that you understand each and every step.

Q: 은 J4-√x dx

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

Q: In a polynomial, a number in front of the variable is called exponent. صواب ( خطأ

A: Given ,  In a polynomial , a number in front of the variable is called exponent  We have to tell it…

Q: Consider the function f(x) = x^4 − 5x^3 + 9x^2 Find a)  The intervals on which f is increasing. b)…

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Q: For questions no. 2 and 3. Given: A thermometer reading is 60°F at 3:00AM and a Civil Engineering…

A: From Newton’s Law of Cooling, we know that: T(t) = Ts + (To – Ts) e-kt Where, t = time, T(t) =…

Q: height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t)= - 16t²…

A: Velocity

Q: 2. (D³6D2 + 12D - 8)y = 0

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Q: II. Solve the following problems. Enclose final answer. 9. A gutter with trapezoidal cross section…

A: Concept: Area of the base of the trapezoid =12(sum of its opposite sides)×height We know that the…

Q: Expand the quotient by partial fractions. x²+3 x² - 13x+42 ²+3 x²-13x+42 (Simplify your answer.)

A: Given :x2+3x2-13x+42

Q: y = x and y = x²

A: We will use simple Integration rules to find the area of the region bounded by the curves y=x and y=…

Q: (√²+2) dt

A: We have to integrate to given function

Q: y = (x²+1)4 (2x + 1)² (3x − 1)5

A: We have to find derivative

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Q: 15. The sides of a triangle have lengths x, x + 4, and 20. Specify those values of x for which the…

A: Concept: Parallelogram Properties: A Parallelogram is a particular polygon formed by a quadrilateral…

Q: Lim x-0 e³ +ex -x²-2 sin² x-x²

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Q: 3√3 dx X²³√x² +9

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Q: dy 9 Find the general solution of the differential equation: - dt t Use lower case c for constant in…

A: Here we have to find the general solution of the given differential equation,  dydt-9t·y=t5 Compare…

Q: 5. Given z = arctan (), Find əz/ay

A: We can answer the question as below.

Q: 2. Two vectors, and b are placed tail to tail and have magnitudes of 2 and 5 respectively. There is…

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Q: The solution set of the equation x2=12-4x is {2,6} صواب خطأ

A: The given equation is: x2=12-4x  ...(1)

Q: 16 The range of the function f (x)=6x-8 is all integers numbers. صواب O خطأ

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Q: Find the derivative of f (y) = 2 sin6 (y8). Enclose arguments of functions in parentheses. For…

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Q: The scientific notation of the number 0.0023 is 2.3x10-3 صواب خطأ

A: The given number is 0.0023We need to write the scientific notation of the number 0.0023

Q: The graph of a rational function, f(x), has a point of discontinuity when x = 2 and an asymptote…

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Q: 2e^xdx-3e^ydy=0   Find y(x) and f(x,y)

A: Follow the procedure given below.

Q: Lim √2+x² X

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Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

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Q: 3 Find the approximate value of fe-x² d x, by using the Simpson's rule with n = 8. Click here to…

A: As we know from the Simpson's rule: ∫abfxdx=∆x3fx0+4x1+2fx2+4fx3+2fx4+...+4fxn-3+2fxn-2+4fxn-1+fxn…

Q: Sx√x +Tdx

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Q: Find x, y and z, if the matrix A = a) x= 2₁ y= V₁ = √3 b) √√6 =√², y = x= 2= c) None of these d)…

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Q: Find the integral for the area of the region bounded by y = 2x+4, y = 2-3x, and y = -x using a…

A: Using vertical strip form double integral then integrate

Q: Find the average value of the function f(p, ,0) = p over the solid ball p ≤7. (Simplify your answer.…

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Q: For f (x)=xl-2, then f(-2) =0 صواب

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Q: 3. The Critical Point of y=xe*

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Q: Consider this expression: sin (-9) Reminders: To indicate √√7, then type: sqrt(7). You must type the…

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Q: for a system of two equations in two variables, the graph of the equations are the same lines, then…

A: We have to find out the solution existence

Q: Evaluate the integral directly by integration with respect to x and y. 7 x=(y/5)+1 5x-y S S dxdy…

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Q: ƒ (x, y) = ln (√√x²y³) f

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curve about the…

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Q: Let R(t) = (t²,1 − t², t) and r(t) = cost. Determine the parametric equations of the line tangent to…

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 3. Lim In(x+1)3 X48 6x 3

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