Find the total area enclosed between y = x and y = x over th- %3D interval [-1,6]. NOTE: Enter the exact answer.

Q: Using Integration By Parts, x sec - x tan x dx = %3D

A: Use integration by parts.

Q: sin(x)cos(2x)sin(3x) dx o sin(3x)cos(3x) sin(2x)cos(2x) sin(2x) + C 4 12 8 8 sin(6x) sin(2x)…

A: Solving the problem by finding the integration of the problem.

Q: To evaluate x² /1-x² dx using trigonometric substitution, what is the new integral in terms of 0 ? A…

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Q: 3. CHOOSE ONE. Assume that r0. 5x (a) Transform the Cartesian equation = 5x – 5xy into a polar…

A: A)5x2x2+2y2=5x-5xy12x2+2y2=1-yx=r cosθ, y=r sinθx2+y2=r212r2=1-1(rsinθ)r sinθ=1-12r22r2-1=2r3…

Q: The result of dx IS F(b) – F(a), where Fla) and F(b) are real numbers. What is the value of F(b)?…

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Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

A: ∫f(x) dx=∫ 5-31+x2-1dx=∫ 5dx-∫ 31+x2-1dx=5x-3arctanxAdd a constant to the solution=5x-3arctanx+C…

Q: What change of variables is suggested by an integral containing * Vx² – 4? O a cosø O none of the…

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Q: Find 8²-45+13 2

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Q: V14 _13. Given the function f(x,y, z) = e3xyz sin 2xy where x = r² + t² , y = t² +r , z = r+t. Then…

A: Given f(x,y,z)=e3xyz sin2xyx=r2+t2y=t2+rz=r+t

Q: Consider the Cardioid r = 2 − 2 sin θ. (a) Find its total arc length. (b) Determine the area of the…

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Q: Use polar coordinate to evaluate (x² + y* )² dx dy . Leave your answer correct to two decimal…

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Q: 1. Suppose the odometer on our car is broken and we want to estimate the distance driven over a 30…

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Q: dy Do not simplify your answers. dx 3. Solve for sec(3r? + In 2) evz+2 +9 (5x-1 – 3")* e3z Vcot() C.…

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Q: J sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) , sin(2x)cos(2x) , sin(2x) + + C 12 8 8 4 sin(6x)_ sin(2x)…

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Q: Find the tangent to y = x-x+10 at x 3.

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Q: (2x + 4) + 1 (2x +4) +1 dx: x2 + 4x + 5 x2 + 2x- 10 2 2 2 Consider dx = x2 (x2 + 4x + 5) dx evaluate…

A: We can solve as follows

Q: 2x How many times will you use integration by parts in solving- cos²(2x) once O twice O thrice no…

A: Here, the given integral is: I=∫2xcos2(2x)dx=2∫x sec2(2x) dx

Q: 7 -4 Consider the surface x'z* + sin(y zª) + 9 = 0. Use implicit differentiation to find the…

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Q: Consider the following function. f(x) = 2x3 - 12x² + 18x – 7 Find the derivative. f'(x) = Find any…

A: The given function is: f(x)=2x3-12x2+18x-7

Q: Evaluate the integral 20 2) dr by making the substitution u 2. NOTE: Your answer should be in terms…

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Q: x² + 2x- 10 (2 dx = x² (x² + 4x + 5) (2x + 4) + 1) (2x+ 4) +1) x2 + 4x + 5 x2 2 Consider dx -…

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Q: 耳 ixn=wyr Show that d P

A: Given a function is two variables.

Q: Find an antiderivative of the function. (Remember to use absolute values where appropriate.) (a)…

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Q: 1. Evaluate the following limits. 4x – 7 3x2 – 2r – 5 1 c. lim I-1- |I + ¤|

A: We put the limit .

Q: Given x sin (yz) + y³ cos (xz) + z sin (xy) = v3. Find əx (a) implicit differentiation, (b) by…

A: a) Implicit differentiation: We will treat y as constant.…

Q: 3x + 7x + 28 -dx x² + x³ + 7x Using partial fraction, evaluate

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Q: ,2 dx The result of IS F(b) – F(a), where Fla) and F(b) are both real numbers. What is the value of…

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Q: Find the derivative of y with respect to t. y = In (t) dy %3D dt

A: Given function y=lnt9 we have to find derivative of y with respect to t. ln is natural logarithm…

Q: dx The result of is F(b) – F(a), where F(a) and F(b) are both real numbers. What is the value of F…

A: integration

Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. lim…

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Q: 12-11= Sin(z)

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Q: By about how much will g(x,y,z) = x + x cos z -y sin z + y change if the point P(x,y,z) moves from…

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Q: 15х2 — х3— 43х - 19 The integral | can be rewritten as (x + 1)²(x² – 6x + 13) Ах + B C D lax² + bx +…

A: Follow the procedure given below.

Q: cos. Given: tan x |dx. Using trigonometric transformation , the integral in terms of u is m ( u ™ )…

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Q: 4. The surface described by the equation x2 + y + z² = 0 is a(an) (a) elliptic paraboloid symmetric…

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Q: 3. Evaluate the lim(2x – 7). x-4 а. lim(2x — 7) %3D 2 x-4 b. lim(2x – 7) = 1 с. lim(2x - 7) %3D7 x-4…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Evaluate the integral. dx :+ C J 22 Va2 – 36 x² /x? - NOTE: Enter the fully simplified answer with…

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Q: Find the first and the second derivatives of the function. y%3D 6-x

A: The given function is: y=x6-x  =-xx-6  =-x-6+6x-6  =-1+6x-6  =-1-6x-6

Q: 3. Sin x dx 3- COS

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Q: Find the area: y = sin x, the x-axis, the y-axis and the vertical line x = 2 *

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Q: discuss and sketch the graph of the given function f (x) = e" + x %3D

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find the indefinite integral using the formulas from Theorem 5.25. (Use C for the constant of…

A: We need to evaluate integral.

Q: Find the points on the ellipse 5x2 + y² = 5 that are farthest away from the point (1, 0). smaller…

A: To find the points on the ellipse 5x2+y2=5, that are farthest away from the point 1, 0.

Q: Solve the following problems. 1. Name and sketch the graph of y² = z in R³. II.

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Q: dx Using Trigonometric Substitution find f(0) 3 (x² + x + 1) 2 4 3 sec? e O 3 sec? e 4 O 3 sec e 4 3…

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Q: 3(x + 2)\/1 (x+2)² Which of the following is *+2) + arcsin 9 +C equal to? arcsin (z + 2) + (x + 2)v5…

A: Given that,     92arcsinx+22+3x+21-x+2292+C

Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the y y = 5 x-x…

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Q: 2 Evaluate V4-x² dy dx using polar 2x-x2 Coordinates.

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Q: AY Deternine the elative maxina and relative Minima, If any.

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Q: 2) Convert the following rectangular equations to polar equations. a) x² - y = 3y b. 9xy = 1

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