Evaluate the definite integral. NOTE: Enter the exact answer. 10 S™ ||ti + 1²i|| dt

Q: ∫sinx sin(cosx) dx

A: ∫sinxsincosxdxLet u=cosx=∫ -sinudu=-∫sinudu=--cosuSubstitute back u=cosx=--coscosx=coscosxAdd a…

Q: Find f'(x) from f(x)= = 2x³x²x+ 2 using the definition of a derivative. (Do not include "f'(x) =" in…

A: Use simple differentiation formula.

Q: Find y = f(x) given d²y dx² = 5x² + 2

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Q: Solve the following differential equations 1. (D^2 - 3D +2) y = 2e^-x + 8 2. (D^2 - 4) y = 8e^2x -…

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Q: The gravitational force, F, between an object and the Earth is inversely proportional to the square…

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Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

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Q: e the polynomial equation by using the root method, and check the solutions graphically. 3x³-192=0…

A: Given query is to find solution of the polynomial.

Q: A point starts at (x, y) = (6,0) and moves CCW along a circular path centered at (x, y) = (0, 0).…

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Q: 3) Suppose g(t) = 1/t represents the position, in meters from the starting point, of some object…

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Q: Compute the flux of the vector field F = 2xi + 2yj through the surface S, which is the part of the…

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Q: d Calculateri(t) r2(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and then…

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Q: KE-5 f(x) g(x) Find the area enclosed between f(x) = 0.6x² + 10 and g(x) = x from x = −5 to x = 3.

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Q: th is the graph of the original function and which is the graph of the derivative? g f is the…

A: Given the query is to find which graph is  function and which one is derivative.

Q: Use a computer algebra system to graph f and to find f' and f". Use graphs of these derivatives to…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

Q: Question The total monthly cost of a family plan depends on the number of phones, p, and the GB of…

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Q: x1/2 dx x3/4 + 1 Let x = z8 dx = 8z7dz Is the substitution the most appropriate one? Explain your…

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Q: 2x + 7 f(x) 5x - 10 Step 2 of 2: Evaluate f" (1),f"(-5), and f" (7), if they exist. If they do not…

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Q: * Using trigonometric substitution to evaluate: find dx √ dx, √2x²-4x-7 (3√2)/2 cosø dø O (3√2)/2…

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Q: Let f(x) = x² - 1 on [-2, 3], Part A: What is the slope of the secant line connecting the function…

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Q: The revenue from the sale of a product is given by the function R = 5000x-0.1x³ dollars. Use…

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Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: Use a graph to give a rough estimate of the area of the region that lies beneath the given curve.…

A: To the find the rough estimate of area of region that lies beneath the given curve and the exact…

Q: Given the sequence by defined recursively below, find b4. b₁ = 2 bn = 3bn-1 - 1 Provide your answer…

A: We have to find forth term of the sequence

Q: Solve the equation. Give your answer correct to 3 decimal places. 10,000 = 1500e0.07x

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Q: 1. fx² In x dx = f x² dx f In x dx (In x − 1) + C Is the solution correct? If your answer is yes,…

A: We have to give reason and then solve the integration .

Q: The base of a certain solid is the area bounded above by the graph of y = f(x) = 9 and below by the…

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Q: Use the given graph of the polynomial function to complete the following. a. Estimate the…

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Q: 3.x√x² + 1dx

A: Given query is to find the value of the integral.

Q: ∫esin4xcos4x dx

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Q: ∫(tan2x+cot2x+4)dx

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Q: 4- 3- 2- 1- X▶ 1 2 3 ZA 10 4 13 3 P 2 Ty 1

A: we have given 3D cartesian coordinate system

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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

Q: x +4 1. √x dx 2. √ 1 + √F 1+ 3.x√ √x² + 1dx -dx

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Q: -cosh(2x² + 1). Evaluate (A) 4xsinh(2x² + 1) B 2xsinh(2x²+1) C) xsinh(2x2 +1) с D (2x2 + 1)sinh(2x +…

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Q: A toy racecar moves along a circular track with a radius 3.4 feet long and starts at the 3-o'clock…

A: We can solve as follows

Q: Tutorial Exercise A force of 9 lb is required to hold a spring stretched 3 in. beyond its natural…

A: 1 in = 1/12 ft

Q: Points A and B are separated by a lake. To find the distance between them, a surveyor locates a…

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Q: long as 1 235 times as long 235 times as long 235 times as long 360 235 times as long 2π 360 times…

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Q: 1. x +4 √x -dx

A: We will use substitution method.

Q: Consider the surface of equation z = x2 + y² . What is the equation for the tangent line to S at the…

A: We need to find equation of tangent line.

Q: J 2x - 11 dx 2 x²+x-6

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Q: The figure in this exercise shows a horizontal layer of the vector field of a fluid flow in which…

A: This is a problem related to vector field. Based on the formula and concept we will answer the…

Q: Water is flowing into a tank at a rate of r(t) = 3√2 cubic meters per minute. How much water entered…

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Q: Describe the graph of the equation. r = − 17i + tj + (t²-1) k It is a parabola in the x = It is a…

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Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t…

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Q: A rectangular box is designed to have a square base and an open top. The volume is to be 1372 cm³.…

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Q: 19T (a) Find an angle between 0 and 27 that is coterminal with 10 (b) Find an angle between 0° and…

A: Here we have to find the coterminal angle.

Q: @[² (d) √x-x (x² + y²)³/2 dy dx.

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: Get the aame answer written in bracket of (d) it is correct

Q: A sample of a newly discovered element, West Virginium, has a half-life of 295 years. How long will…

A: We have to find out t