Evaluate the following integral 5 – 2x (c) dx 2/3x – x²

Q: Activity 1. Find the derivative of the following trigonometric functions and simplify if possible. B...

A: Note:as per our answering guideline we can allow to solve only subparts so please repost another sub...

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Q: rectangle. y = 2/x, y = 4/x², x = 6 y y 35 30 25 -1 20 -2 15 -3 10 5 1 2 4 6 -5- y 5- 2 4 4 -2 3 -4 ...

A: Given problem:- Sketch the region enclosed by the given curves. Decide whether to integrate with res...

Q: Find the integral. In 8x dx

A: I=∫ ln 8xx dxln 8x =t18x(8) dx = dtdxx =dt

Q: dx Perform the Integrations 1+ sin x+ cos x Use the editor to format your answer

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Q: dy 3 - dx2 4 y = 1/2 dy/dx = -1 when x = 1

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Q: 1) An equilateral triangular plate with 6m side is submerged vertically in a tank of water so that i...

A: Here, the top surface of the triangle plate is 2m  below the free surface of the water. Therefore, ...

Q: Find the length of the curve: a = t°, y = *; 0<t< v120 3t Find the length of the curve: x = t°, y = ...

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Q: Evaluate the integral sinh? (2x)cosh (2x) cx .

A: Let's find. 

Q: 0. Find the area enehred by the following curves: * =y-2 and X =y.

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 2j as a...

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Q: '5 '5 A function y = f(x) is continuous and differentiable on the interval (0, 7). If f(x) dx = 10, ...

A: Given problem:-

Q: cot5 z csc³ zdz z csc

A: Given :∫cot5z csc3z dz

Q: Determine the volume of the solid by rotating the region bound from y=sin(pi*x/2) & y = x2 from x = ...

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Q: If y = 4x³ + 2x² + 11, find the approximate value of y when x = 2.01, using differentials.

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: This question is related to sequence and series, we will solve it using given information. 

Q: A solid lies between planes perpendicular to the x-axis at x= -5 and x= 5. The cross-sections perpen...

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Q: y³e-2y dy

A: Given :∫y3e-2ydy

Q: 6. S sin2xdr sin'r-4

A: We will use partial fraction to solve th integration after substitution. Which is as follows 

Q: Let V represent the volume of a sphere with radiusr mm. Write an equation for V (in mm) in terms of ...

A: Please see the answer below.

Q: P(x)= x^3-2x-4 a) factor P into linear and irreducible quadratic factors with real coefficients  b...

A: Here, the given polynomial is: P(x)=x3-2x-4

Q: 1. S 4x-5 dx - partial fraction 2x2 +4x-6

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Q: 8. ye = In(xy) 9. (y – 5)2 = 8(x – 3) 10. 2x – xy? +y³ = 0 11. x2 - y? = 7

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Q: If f (x) =2r3+6x- 2, then what is f'(1)? %3D

A: We know that; The Sum/difference rule; f±g'=f'±g' The Power law; ddxxn=nxn-1 And c·f'=c·f' ; where c...

Q: Evaluate: S,(3y6 + 8y* – 9y?)dy -2

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Q: Question 9 12 Let Fx) be an antiderivative of fx), with F(12) = 12 and f (x) dx = 9. what is F(6) = ...

A: Given: fx=F'x  And F12=12 ; ∫612fxdx=9   From the fundamental theorem of calculus; If dFxdx=fx then,...

Q: SOLVE THE TRIGONOMETRIC EQUATION a. V3cosxcscx = 2cosx

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: da 3. S algebraic substitution (x-3) Va-4

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Q: Consider the initial value problem my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of...

A: To solve the initial value problem.

Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8xy? = 2y6 + 1...

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Q: the integral expression on the left to an equal expression on the right. (cos(x)-cos(7x))dx ots Subm...

A: We will solve the integral. 

Q: 19) Find [sin( x9+ 9x) ]' = _by Chain Rule A) 9x8sin ( x9+ 9x) C) 9(x8+1) cos x 19) B) -9 x sin ( x9...

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Q: Find the area of the triangle with vertices P(1,6, -5), Q(0,0,0) and R(4, 6, 1). NOTE: Enter the exa...

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Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

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Q: Find the area of the region between the parabola y = 9 - x and the x-axis. Round your answer to thre...

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Q: Evaluate: (4) S esc" (a) (2x +1) dx C6) Syos y dy

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Q: За—11 dx - partial fractic 2x2-a-6

A: We will solve the problem using partial fraction. 

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. xe 401x dx ...

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Q: What is the area under one crest of the sine curve, from x = O to x = n? y=sin x dx 1/2

A: Given problem:-

Q: A radioactive substance has a half-life of 29 years. What percent remains 80 years after being to it...

A: We will find the remains after 80 years in percentage. 

Q: rotated about the x- axis

A: Solution is here 

Q: 30% of a radioactive substance has decayed after 10years, what is its half-life? 15.9 years 16.7 yea...

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Q: Find the general term of the sequence, starting with n = 1, determine whether the sequence converges...

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Q: Complete the sentence the below. If the point (4, - 1) is a point on the graph of f then f(-)= If th...

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Q: A drug response curve describes the level of medication in the bloodstream after a drug is administe...

A: Given: The function to model the response curve is St=AtPe-kt where t is measured in minutes. It is ...

Q: Question 13 Evaluate the integral J sinh? (2x)cosh(2x) dc sinh“(2x) +C A sinh(2x) +C B 9 costf(2x) +...

A: Use the derivative identity, ddx(sinh(ax))=acosh(ax) And the power rule of integration is: ∫xndx=xn+...