Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx

Q: 16. J x² 4 + x² dx

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Q: d S[e-In(2t+1)]dr. find g(x) - dx A e-In(2x+1) 2 B (2x + 1)² (2x + 1)² (2x+1)² If g(x) = D

A: We have to find out the derivative

Q: Let g(x)=6x-4. Find g (Type an integer or a fraction.)

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Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

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Q: Find the general solution of the given system. dx - 2x + 3y dt dy dt - 6x + 5y Ex(t), y(t)) 0

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Q: Find the area bounded by : f(x)=e*, g(x) = e¯* and x = 3. A (e²-1)² e2 sq. units (e²+ 1)² e2 (e³-1)²…

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Q: Question 19 : The area of a healing wound is given by A=πr2. The radius is decreasing at the rate of…

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0₂ (A) 1 (B) none may vary…

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Q: Determine the area bounded by the functions f(x) = (x+1)³ and g(x)=x+1, 3 (A) Žunit² 1 -unit² -unit²…

A: We need to find area.

Q: 10. y (e-3x+4 +2)/(e2+3x +1)

A: The given function is ; y=(e-3x+4+2)/(e2+3x+1).

Q: The region is bounded by y = x² - 9 and y = x + 3, find the area.

A: Solve the following

Q: C. Determine the Laplace transform of the following function f(x)=x² 1. 2. f(x) = ex, a ER

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Q: Find the area enclosed by r = 2 sin 30.

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Q: lim x-2 x²+2x-8 x-2

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Q: (b)show that: I(cosh at cos at) s*+40*

A: Solution is here

Q: хра (q

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Q: If g(x) == [e'-In(2t+1)]dt, find g''(x) . dx A ex-In(2x+1) 4 B (2x+1)² 4 (2x + 1)² 2 D (2x + 1)²

A: Here given that: g(x)=ddx∫-1xet-ln(2t-1)dt Using the Fundamental Theorem of Calculus: g(x)=ex-ln…

Q: 8. Graph the rational function. horizontal asymptotes. 3x-12 a. r(x)= x+1 Show clearly all x- and…

A: Graphs are to be drawn first and then asymptotes and intercepts need to be marked.

Q: Evaluate the integral: A B C D 16 1 "Im =|m 1 7/6 دان داww 3 sin(3x)cos(3x) dx

A: We have to find out integral

Q: Where is f(a) not continuous?

A: Given:

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3

A:

Q: Find the slope, if it exists. x = -6 Select the correct choice below and fill in any answer boxes…

A: Given x=-6 The graph is

Q: Please show work in terms of d(variable)/dt, thank you! Water stored in an inverted right circular…

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Q: 8) 3 3√3 2² 72

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Q: 3 Evaluate the triple integral: (x+y+z)dydxdz A) 12 B) 24 с 6 (D) 18

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Q: Use of an Auxiliary Variable Solve the equation. The sum of two positive numbers is 2. Find the…

A: see below the calculation

Q: y=1/x²₁ y = 8x₁ y=x/8

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Q: Determine the area of the region bounded by 3x - 5y + 4 = 0 and y-axis from y = 2 to y = 5.

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

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Q: Verify that 2+ ?х ду 2+ дудх : for f(x, y) = 2x³y6 – 4x5y4.

A: Partial differential.

Q: f(x) = 4x²8x +3 x ² + x - 12 2

A: Given.

Q: 3) x² + y² + 16x+10y+80= 0

A: Given

Q: Consider the spherical equation given by p = 4 cos sin p. Determine its corre- sponding equation in…

A: Given

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

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Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: Topic:- application of integration

Q: A lighthouse is on an island 350 meters east of the shore of Lake Bella. The lighthouse beam makes a…

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Q: 12-f(t)= -31 e-³¹ sin 2t t

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Q: B-Find the center of mass of the region bounded above by the half circle y = √ Na²-x² and below by…

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Q: 3. Use appropriate differentiation techniques to determine the first derivatives of the following…

A: see below the answer and calculation

Q: To evaluate the integral [ sin³@cos³0d0 by trigonometric transformation, we use the identity; 1 +…

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Q: . Evaluate 1 4-x² dx

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Q: 9 Let the integral be solvable' using trigonometric substitution. What is the correct choice of u…

A: A detailed solution is given below.

Q: Evaluate the double integral: 2 √² √ (3x² +9y²) dxdy A 40 B 30 C 60 D 80

A: Double Integration by iteration:

Q: dx secx + 1 Transforming - -z² A 1+z² B z²+z 1-z² 1+z² Ⓒ 1- D √ -dz -dz -dz - 2z² 1+z² -dz using…

A: Here, the given integral is: I=∫dxsec…

Q: -x/3 Jx/4 cscxcotxdx

A: topic- definite integral

Q: b)show that: I(cosh at cos at) = 5²440*

A: This is a problem related to laplase transform. Here we will use convolution theorem for evaluating…

Q: f(x) = 5x² - 8x + 15 3x² + 6x 12

A: here first we have  to find domain of function  here domain is which value we can put in function so…

Q: Find the domain of the following function. 9 f(x)=- 2 36-x The domain is (Type your answer in…

A: Use the definition of domain of function

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: C option is false.

Q: 4. f(x) = √3x5 - 2x + 7x²= 18x-25

A: