1. Find the area of the region bounded by y = x^2 + 2x -6 and y = 3x.

Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

A: To Find:Set up the integral for the work done in pumping the content to a point 3m from the top of…

Q: Q2/A) Solve the following differential equation x²(y + 1)dx + y²(x - 1)dy = 0 DE

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Q: Find the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -…

A: equation of tangent is : z-z0 = m (y-y0)

Q: 18. f(tan 2x + cot 2x)² dx

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Q: Evaluate: (7-j3)ln(cosh(2+j5))

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Q: How do you multiply cube in an equation?

A: Solution

Q: Evaluate the following. 1. [(sec 3x+cos3x)² dx

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Q: y= 3x²-1 2 2x+5

A: Given problem:- y=(3x2-1)/(2x+5)   Find derivative using quotient or product rule

Q: Evaluate the following. 3 1. f(1-√x) dx √X

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Q: = 2x tan

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Q: 9. [cos° { xsin’ } xdx

A: The objective of the question is evaluate the indefinite integral.

Q: f(x) = (6x² - 2x+1)^

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Q: Change the order of integration of the iterated double integral: -8 r2 To for Y dx dy. 1/3 x7 +1…

A: Let's change the order of given integration.

Q: Given: 3z = xy Find fy O xy/3 Oy/3 Ox/3 O None of the choices

A: We can find the partial derivative as below

Q: Determine the area of region by y = x^2 + 4x and the y - axis

A: Area between the y=x^2+4x and y-axis is unbounded .  So, we will find the area bounded by the region…

Q: (D³ - 3D²D + 3)y = 0

A: The given differential equation is: D3-3D2-D+3y=0   So, the auxiliary equation is: m3-3m2-m+3=0

Q: s 3x5 3x4+6x³-3x2 - 6x Evaluate x²–2x Α) +In x² - 4x Ⓒ²-*** B + In 2 x²-2x-In x² - 4x 2 dx. using…

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Q: Question 2 S y dy Find √x+2 A ² (√x+2-5) (5√/y+2+y+24) + C 3 ℗ ²² (√5+2-5) (5√/y+2+y+21) + C B…

A: GIVEN

Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: fax² ax² + bx dx is equal to O ax³ bx² ㅇㅇ + C 3 2 ax³ bx² 3 2 a²x³ 6²x² 3 2 a²x² 6²² 3 2 O + + + +…

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Q: 5. Evaluate , x dV where S is the region (solid) bounded by x = 0 and x =

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Q: Using Newton's method with an initial approximation of x₁ = 2, what is the second approximation x₂…

A: As we know the integration formula for the Newton's method. xi+1=xi-fxif'xi where i=0,1,2,3.....…

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: Given:         Density of Liquid ρ=9000 N/m3          Sides of triangle a=2 m     The expression for…

Q: 1. Let S be the solid of integration of the ff. integral Q. Sketch S and label its boundaries.…

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Q: 50 [" (ax³ + bx² + cx) dx=2b -50 A) True B) False 50 x²dx

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Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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Q: A payment of $25,000 is due today. What three equal payments, one in 2 years, one in 4 years, and…

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Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

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Q: (D³ - 2D + 4)y=0; y = -2, Dy = 8, D²y = 0, when x = 0.

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Q: y = 4 16 3x+3

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Q: What is the value of f(1) - 168 in x³ Inx dx = f(x) ((1/4) Inx-B) + C? 0 2 0 3 01

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Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx-

A: To evaluate we first multiply and divide by 2 the given function.  Then use the formula: 2(sin(mx)…

Q: 3x5 Evaluate 3x4+6x3-3x2 - 6x ^ x² = 4x + 1 [ (x-1) 1/6 (x + 2) 16/3] + A In +C 2 1/2 16/3 B -2x-In…

A: Given that       ∫3x53x4+6x3-3x2-6xdx  We can re-structure this integral as…

Q: 12. 4 CSC X cot² x dx

A: Given problem:-

Q: What will be the rate of change of the volume of a sphere with respect to its radius when the radius…

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Q: 15. [sec xdx

A: Trigonometric Identity: sec2x=1+tan2x

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by , the x-axis, and…

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Q: What is the value of f(1) - 16B in fx³ Inx dx = f(x) ((1/4) Inx-B) + C? (A) 2 B 3 C 0 D 1

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Q: Evaluate sin (Inx) dx. Integration by parts will be used repeatedly. What is the expression after…

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Q: What is the dy/dx of y = 3sin²x cos x ? O 3 sin x(sin²x - 2cos²x) O-3 sin x(sin²x - 2cos²x) O 3 sin…

A: Given: y=3sin2⁡xcos⁡x To find: dydx We know that ddxcosx = -sinx ; ddxsinx = cosx

Q: Applying basic rules of Differentiation. Evaluate and Solve the function using the product or…

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Q: QUESTION 14 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)…

A: We need to find area.

Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

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Q: 4 -4 x3 16-x² dx is equal to

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Q: t'dt √4+1² 19 dt

A: We have to evaluate ∫02t34+t2dt.

Q: S₁ 2 63 Evaluate: A 16 B 105 C) None 16″ D 105 2π E 63 sinxcos³xdx is equal to

A: We can find the integration as below

Q: 4. t²dt /t° +1 3√/₁³

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Q: √ ² si 2 63 16 105 2n C 63 D) None Evaluate: A (B 2 sinxcos³xdx is equal to

A: Given query is to find the integral.

Q: Which of the following statements is NOT true about the derivative of the function? The derivative…

A: The geometrical meaning of derivative is , the slope of the line segment tangent to the function…

Q: What should be the shape of an oval field complying to a given circumference, if it is to have a…

A: Given :The shape of an oval field complying to a given circumference, if it is to have a maximum…