Differentiate the following functions using Chain Rule: 1. y = (4x + 3)²

Q: Evaluate tan" (x) sec¹x dx. 1 1 (A) -tan (m+2)(x) +· ¹tan" (x) + C - m+2 m 1 1 (в -tan (m+3)(x) +…

A: On solving this we will get Option (B) is correct

Q: In a basketball league consisting of 12 teams, each team plays each of the other teams exactly…

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Q: The integral dx (x²+4)² sec ³0 de sin ²0 de ° csc ³0 de ° Scos²0 do can be transformed to which of…

A: Here we have to transformed the given integral.

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

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Q: y=(-4x²-5x²) (7x - 2)

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Q: Find the area bounded by the trigonometric curves 5ñ to - 4 3.667 square units 3.459 square units…

A: topic- area bounded by curves

Q: Covered topics are Applications of Definite Integral: Plane Areas and Areas Between Curves and…

A: We have to find volume generated by given condition.

Q: Suppose m and n are constants and m‡n. Evaluate [sin(mx) sin (mx) cos(nx) dx 1 _____cos (mn)x -…

A: We have to solve integration

Q: Exercises To Solve [No.5] 3dx 9x²-6X+5 1

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Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

A: Given

Q: Question 11 Evaluate €S= A B C D 3x5 3x4+6x³-3x² - 6x x²-2x-In x² - 4x 2 x² - 2x 2 x² - 4x + In +…

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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: 13. - (In t ² )º t dt

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Q: Find y dy √x+2 using the substitution u +5=√√√y+2.

A: We will evaluate the given integral by using substitution method as shown below

Q: QUESTION 12 x 1/2 ·S For S S- S- dx and using the substitution=x1/2, the resulting integral takes…

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Q: Which of the following equations correctly states the Product Rule of Differentiation? dy = = f(x)g…

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

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Q: 2. [e1/² cos 2tdt Set/2

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Q: Use the table to the right to find the given derivative. d[ f(x) dx x + 7 X = 5 = (Simplify your…

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Q: using the substitution +5= √√x+2+ Find y+2 (√y+2-5) (5√/y+2-y+24) +C 02 (√3+2-5) (5√y+2+y+21)+C…

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

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Q: Equation xdy + ydx = 0 y"-3y" + 3y + y = 0 (y)¹/² = √/(1+y")4 Order Degree Kind IV DV

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

A: We need to integrate the given function with integration by parts.   We will do it twice

Q: π 5π Find the area bounded by the trigonometric curves y=sinx and y=cosx from x== to x== 4 4 (A)…

A: The region bounded by the curves y=sinx and y=cosx from x=π4 to x=5π4

Q: Л 5x Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=-tox= 4 4 A 1.414…

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Q: 19. dx 1 Je²x_8 2x -8

A: The solution is given in the next steps.

Q: If a particle moves on a straight line so that s = et (cost – sint) . Which expression can be used…

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Q: π Find the area bounded by the trigonometric curves y = sinx and y=cosx" from X=- 3.459 square units…

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Q: 4 b. [√x ln xdx, 1 4 ㅠ C. fx√4-xdx, d. fx sin (2x) dx. 0

A: Solve the following

Q: ·S- A 4u B [4-(2u²) ² C) -du V 4u Ⓒ* D -du 4 For x 1/2 -dx and using the substitution u=x1/2, the…

A: We have to solve above integral

Q: What is the solution to the differential equation 2√√ay- da Oy = ( ² √₂-2) ? 3 Oy=(2²√x - 2) ³ 1 =…

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Q: 1 Find the area bounded by the curve y=- =-=-—-—-x³-3³² x ² + 16 4 -x2 + 3x and the line y=x.

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Q: For x 1/2 -dx and using the substitution u=x 1/2, the resulting integral takes the form: x-x 4u -du…

A: We can rewrite the given integral by using this substitution u = x1/2

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: Consider S integral can be written as of A, B, and C. 6 O 5 14/3 O 17/6 3x5 3x4+6x3-3x2 - 6x √(x-1…

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Q: 11. fel/x²di .3 X хр

A: Here, to evaluate: I=∫e1x2x3dx

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

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Q: QUESTION 2 Evaluate lim " QUESTION 3 Clearly illustrate with explanations why lim 100 0.01F g(x) x-0…

A: We have to find limit

Q: Which of the following is a polynomial function? C. 2x+7 A. g(x)=√x-7 y = B. f(x)=2*-5 D.…

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Question 12 Consider ·S S(x-1 x-m+ (A) 17/6 B) 14/3 6 D) 5 3x5 3x4+6x²-3x² - 6x A B C + -+ x-1 x+1…

A: Consider ∫3x53x4+6x3-3x2-6x dx. Using the method of partial fractions, the given integral can be…

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

A: I am attaching image so that you understand each and every step.

Q: What is the value of f(1) - 16B in [x³ Inx dx = f(x) ( (1/4) Inx - B) + C? A 3 (в 0 с 2 D 1

A: We have to find the value of f(1) -16B where it is given that  ∫x3lnxdx = f(x){(1/4)lnx - B }+C    @…

Q: 16. Find the area bounded by the curve y=-x³--x²+3x and the line y=x. 16 4

A: 16)Given,y=x316-3x24+3x and y=x

Q: ·S- y dy y+2 A (√3+2-5) (5√3+2-y+24)+C ℗(√9+2-8)(5√3+2+7+21)+C Ⓒ(√3+2-5) (5√3+2+y+24)+C…

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Q: < d dx x² 2 tan t²dt=2x tan.x² (A) True B) False

A: Formula :

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: 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: Find the area bounded by the curve 4 square units O 16 square units O 8 square units 10 square units…

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Q: ‹S- A S Ⓡ /- © /- S- D For dx and using the substitution = x1/2, the resulting integral takes the…

A: Just use the substitution and find the required integral. Option (B) is correct.

Q: 15. cos³ 3x 3√√/sin 3x dx

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