1/B) Find the length of the cardioid 'curve: r = 1 + cose

Q: x2 £f* dx X A) True B False tan 1²d/= 2x tan.x²

A: We have to find derivative of given integral.

Q: 4. f In (2x + 1) dx =

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Q: 4. y = 4x², x = 0, y = 16; about y = 16

A: Volume = ∫ πy2dx here y = 16 -4x2 and limit from x 0 to 2

Q: Question x² Find the lower sum for f(x) = +2 on the interval [-7, -3] using 4 rectangles. 10 10 then…

A: We have to evaluate the area using lower rectangular values.

Q: Problem 1: Use the elementary row or column operations AND cofactor method to find the determinant.…

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Q: y=(-4x²-5x²) (7x - 2)

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Q: Water is flowing into a conical cistern at the rate if 8 cubic m/min. If the height of the inverted…

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Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

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Q: St. -4 16-x² A 4 (В 2 (C) 0 (D) None (Ε 8 00 dx is equal to

A: This is based on the definite integral.

Q: S₁ A B If 2x²+x-2 (x+1)(x²+1) ² 1 -- 2 U NIG 5 —— D E) None + -S₂ -dx = A x + 1 + B (2x) + C x²+1…

A: Partial fraction decomposition

Q: Symmetric equations of a line with direction vector d = (5, 3, -4) and z-intercept of 7.

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Q: 3. f(e-²x - 1) dx

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Q: What is the value of f(1) - 16B in I x³ Inx dx = f(x) ( (1/4) Inx - B) + C? 2 0

A: Given; ∫x3lnxdx=fx14lnx-B+C    ...(1)   First, we have to find the integral value. I=∫x3lnxdx Apply…

Q: sec4 w tan w dw

A: Solution of given question is written in below steps.

Q: QUESTION 13 Is this statement true or false? An infinite sequence (a) is convergent only if lim a, =…

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Q: Determine the volume of the solid obtained by rotating the region bounded by y= x^2 and y=x about…

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: Find the area of the region lying between the inner and outer loops of the limacon r = 1 – 2 sin θ

A: Solution of the problem as follows

Q: If z = x² dz = Az = - ·xy + 4y² and (x, y) changes from (1, −1) to (0.96, −0.95), compare the values…

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Q: 7. [(In x)² dx

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Q: 10. 3 J√cos z sin ³ zdz COS

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Q: S √(x-m+ 3. Consider 3x5 3x4+6x3-3x² - 6x A B C + + x-1 x+1 x+m -dx. Using the method of partial…

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Q: dx 3-2x-x²

A: We need to solve : ∫-10dx3-2x-x2

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: Question 11 [₁ Evaluate: 2 A 63 16 B 105 C) None 16л D 105 2n E 63 sinxcos³xdx is equal to

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Q: If s t5 - 10t², when will the acceleration d² s dt² O2 seconds O 0.5 second O 1.5 seconds 1 second…

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Q: Using chain rule, what is the (2x-¹-3x)³ ? da O 24+108x²+54xª+81x6 x4 -24+36x²+54x4 -81x6 x4 O…

A: The objective of the question is find the derivative .

Q: Find the area bounded by the curve y=- 16 (A) 16 square units B) 10 square units 8 square units D 4…

A: If y=f(x) and y=g(x) are two continuous function on a,b and f(x)≥g(x) on a,b , then area bounded by…

Q: P af af Q3.If f(x,y)=sin(x-3y) + sin(x) find: and əy ax

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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: +√√² cas² S 4 cos²20 de is One of the correct steps to evaluate @ 1²00-1/²160²20 4 de- A sin²20d0 Ⓒ…

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Q: 6x⁹-x5+ 27 A B R C D) 0 E) None K|N 2 4-x² dx is equal to

A: Explanation of the answer is as follows

Q: 50 [" ( ax³ + bx² + cx) dx = 2b = 25 150 x ²6 x²dx -50 0 A) True B False

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Q: 2. Let f(x) = 3 cos 2x + sinx. a) b) Show that f'(x) = -5 sin 2x. π 3π In the interval <x< one…

A: We need to find derivative and normal.

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2=2y, the…

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Q: Evaluate S= 3x5 3x4+6x33x2 - 6x + In O x-2 2 x² - 4x 2 O x² - 4x + In 2 x²-2x-In + In -dx using…

A: Given problem:-

Q: +∞o Evaluate: S e-x dx 0 A + ∞ (divergent) B 0 C 1 D) None E e

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Q: WW |Q3.If f(x,y)=sin²(x−3y)+sin "¹(xy) s fin 34 and 3 dy

A: Given :f(x,y)=sin2(x-3y) + sin-1(xy)

Q: 3x5 S 3x4+6x³-3x2-6x x²-2x = 2 [ (x-1) 1/6 (x+2) 16/3 (x+1) 1/2 ® [ B x² - 4x 2 x-1) 1/6(x+2) 16/…

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Q: Q1/A) Replace the polar equation by equivalent Cartesian equation r2cose +2sing

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: exdx 4-ex

A: We can find the integration as below.

Q: 1. Solid S is bounded by the ff. surfaces. Sketch S and label its boundaries. y = √√√√x² + z², y =…

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

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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: Find 36 zdV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), and (0,0,2) E

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Q: Integrate each of the following. Show complete solution. 1. 1000dx 2. S²x¹ + 3x² + 1)dx 3. f(u² + u…

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Q: 3x5 3x4+6x33x2 - 6x (x-1) 1/6(x+2) 16/3 + In x+1 (x-1) 1/6(x+2) 16/3- (x+1) 1/2 (x-1) 1/6(x+2) 16/3-…

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Q: Consider the curve, x² - y² + sin (TX) In(x) + x = 0. =

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Q: please answer letter b only,

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Q: = 2x tan

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Q: 2x²+x+1 A (x - 1)(x + 1)(x-2) dx = ₁+ A -2 (B) None 3 D E 15 B x+1 + x-2 d. dx, then the value of C…

A: Given  ∫2x2+x+1x-1x+1x-2dx = ∫Ax-1+Bx+1+Cx-2 dx