Can the Fundamental Theorem of Calculus be used to find xcosx²dx?

Q: S sinxdx 7+ cos²x

A: integration ∫sinx7+cos2xdx

Q: c) (Vilntdt ; d) fe' sinxdx ;

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Q: X-25 (x-2) √√x²+2x Converges? Dieverges? dx AND WHY?

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Q: , 103√x - √x X dx

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Q: 7. Use the D-Test to Find the relative extrema and or saddlepoints for the function: f(x, y) = 3xy —…

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Q: 2) Students often make these simple derivatives harder than necessary. How would you differentiate…

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Q: ƒ ( 1 ) = 1 ² 0 1²) find f' (2) (2 decimal places) Using the Product r

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Q: d the indefinite integral using integration by parts with the given choices of u and dv. (Use C for…

A: using  Integral by parts:-  ∫u v dx = u∫v dx −∫u' (∫v dx) dx  here u = ln(x) and v = x^3   u' = 1/x…

Q: Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (1, 2, 2) in the direction…

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Q: 19.) Find the indicated of 0. exact value of the trigonometric function CSC =-9/8, is in quad III 7…

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Q: Question 12 O O Which of the following is equivalent to C ? 10 6 10 C 10 16 C 10 10 C 4

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Q: A ball is shot out of a cannon at ground level. Its height H in feet after t sec is given by the…

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Q: Find the general solution of the given differential equation. dy + (cos³(x))y = 1 dx y(x) = cos²(x)…

A: To find the general solution of the given equation. cos2x sinxdydx+cos3xy=1 To give the largest…

Q: Sketch the curve given by the pair of parametric equations over the given interval x = 4 cost, y = 2…

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Q: Find the general solution of the differential equation y^(4) + y''' + y'' = 0

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Q: Using the same vectors v = (1, 3, 2) and w = (3, 5, 6) and the same point, P = (8, 4,- 2). Find the…

A: We have, vectors v = (1, 3, 2) and w = (3, 5, 6) point,P  = (8, 4,- 2).

Q: In Problems 1-5, let R be the region bounded by y=x² + 3, y = 2x, x = 0, and x = 4. Each problem…

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Q: 20. Find the area of the region between the curve y sin x and y = cos x from 0 to π/2. a. 0.414 b.…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 5. S dx x√16x²-5

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Q: Let f(x) = x³ 3x - 1.5. Determine whether the Intermediate Value Theorem can be used to show that…

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Q: 2. Determine the derivative with respect to x of: a) f(x)=12* - 60

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Q: Suppose f(x)= = -4 6x + 6 Then the expression

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Q: In Problems 11-15, let R be the region bounded by the lines y = -2x-4, y = 6, and x = -2. Each…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: can you explain how you got (x-2)=(t-3) and can you explain how you got the new limits because the…

A: Given:

Q: Part a) Use the steps demonstrated in this module to find an equation for the logarithmic function…

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Q: Given the polar equation r The eccentricity is e = 9 8 + 5 cos(0)' The equation of the directrix is:…

A: Given the polar equation r=98+5 cosθ. To find the eccentricity, equation  of the directrix and to…

Q: Consider the graph of the function f given below. f(x) I -2 4 B) If h(x) 2 0 -2 2 x 4 A) If g(x) =…

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Q: In Problems 6-10, let R be the region bounded by y = x² + 1 and y=x + 1.Each problem will describe a…

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Q: What formula would be used to calculate the middle rectangle approximation Joyx+2dx using four…

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Q: Select the basic integration formula you can use to find the indefinite integral. It cos(5t²) dt of…

A: The indefinite integral is ∫t cos5t2 dt

Q: Find the area of the region under the given curve from 1 to 6. x² + 5 7x - x² y =

A: The given curve is

Q: The subject is: Precalculus The general subject is: Introduction to Calculus and the specific…

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Q: (a) By using substitution method, evaluate (x²³ − 1)² dx.

A: The integral isTo determine: The solution of the integral.

Q: Given the ellipse: (x − 3)² 36 Find the center point: List the four vertices: + (y - 4)² 25 = 1

A: Given the ellipse: x-3236+y-4225=1 To find the center point. To list the four vertices.

Q: Find the annual percentage yield for an investment at the following rates. (a) 7.1% compounded…

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Q: lim x →∞ lim x →∞ 77-3x+71 cx77-71 ax ax77-3x+71 cx74-71 ax74-3x+71 lim x →∞ cx77-71 = AY AY

A: we need to find the given limits

Q: The owner of a skating rink rents the rink for parties at $440 if 20 or fewer skaters attend. For…

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Q: The first line does it read d/dx(x^h)=h*x^h-1 ????

A: The given rule ddxxh=hxh-1. We have to explain the formula.

Q: Find the area enclosed by the ellipse a² b + y=-b√√√a²-x² y² 62 b y=1/√√a²-x² = 1 shown in the…

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Q: How long do you need to invest your money in an account earning an annual interest rate of 5.177%…

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Q: If a company has total costs C(x) = 24,000 + 45x + 0.3x² and total revenues given by R(x) = 425x -…

A: The total cost function is Cx = 24,000+45x+0.3x2 Total revenue function is Rx = 425x-0.7x2 To…

Q: dt t² - 8t + 20 +2

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Q: What is the area between the curves y = -²³ and O 10 -24

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Q: Follow the Steps to Successful Curve Sketching to sketch the graph of f(x)=-4 Show all stens

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Q: dy dx + 2y = x³e-2x

A: The given differential equation is: dydx+2y=x3e-2x

Q: Consider the function: f(x,y)=3xye 8x²-8xy + y²

A: We know that, a function f(x,y) has stationary points at that points where, the partial derivatives…

Q: 3. S sinxdx 7+ cos²x

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Q: The base of a three-dimensional figure is bound by the line x = √√y on the interval [0, 4]. Vertical…

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Q: Use partial fractions to find the area of the given region. 12 x + 5x + 6 y -1 y 3 2 1 -1| 1 2 3 4 5…

A: The region is bounded by the curve y=12x2+5x+6 in the interval 0, 4. To find the area of the region…

Q: A can is filling with water at a rate of r(t) = t² cm³/sec. If the can was empty at t = 0, what…

A: We have,  r(t) = t2 Can was empty at t = 0Amount of water t = 4