y" + 4y= cos²x

Q: Evaluate A B с D S= 3x-5 3x4 + 6x3-3x2 - 6x x² - 4x 2 x² - 2x 2 x² - 4x 2 x2-2x-In (x-1) 1/6(x+2)…

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

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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: 7. fex tan¹(ex dx

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

A: Given ∫sin (ln x) dx Let I=∫sin (ln x) dx By using integration by parts method,∫udv=uv-∫vdu u= sin…

Q: 20. [(x²+2x-10/3 (5x+5)dx

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Q: Evaluate (A) (В B D Stan" (x) see4x dx- 1 m+3 -tan (m+3)(x) + m+1 1 (m+1 1 tan + ¹)(x) − − m+1 m-1 1…

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Q: [³ sin√xcos√x √x 0 A) None Зл B 256 Зл C 512 3 D 256 3 E 512 - dx is equal to

A: Given, ∫0π24sinxcosxxdx

Q: S²- 16-x2 A 2 B) 8 0 None 4 E dx is equal to

A: I am attaching image so that you understand each and every step. Option "C" is correct answer.

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: 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: Evaluation. Find the antiderivative of the following exponential expression. Show complete solution.…

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

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Q: For 1/2 U -dx and using the substitution -du -du 4u √4-(2u²) ² 4u du -du 1/2, the resulting integral…

A: In this question, we want to know the Integral form after substitution.

Q: By method of Integration by Partial Fractions, (x³ +5x²+6) dx (x²–2x+5)² A True B) False A B (2x-2)…

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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…

Q: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

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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: 3x5 3x4+6x33x2 - 6x + In Evaluate S Ox²–2x (x-1) 1/6(x+2) 16/3 (x+1) 1/2 2 Ox²-4x (x-1) 1/6(x+2)…

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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: 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: (в Suppose m and n are constants and m #n. Evaluate 1 (A) √ [n² m² -cos(m− n)x-- -cos(m+n)x] + C m+n…

A: To solve the given integral.

Q: Find S y dy Vy+2 D using the substitution u + 5 = √y+2. A √y+2−5) (5√√y+2+y+24) + C Ⓡ(√9+2-5)…

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Q: ·S- For x1/2 S- S. dx and using the substitution -du U 1-u² 4u -du 4u 4- (21²) ² U -du 1-u4 -du u=x…

A: We have to solve Integral

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: Evaluate Stan" (x) sec¹x dx- 1 A -tan ₂ (m+3)(x) + —_—_—_tan (m+1)(x) + C m+3 m+1 1 1 B −tan…

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Q: x-m+ 3x4+6x3 3x2 - 6x A B C — + x-1 x + 1 x+m +. dx. Find the sum of A, B, and C. D

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Q: If 1500 square centimeters of material is available to make a box with a square base and an open…

A: We can solve the given problem by using the second derivative test.

Q: If 10 f(x) dx = 17 and (A) True (B) False #free f(x) dx = 12, then 10 Sofo f(x) dx=5

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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: Consider 12-1 S= x-m+ 3x5 3x4+6x33x2 - 6x A B C + x-1 x + 1 x+m (A) 14/3 (B) 17/6 C) 5 6 —+ -dx.…

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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: Suppose m and n are constants and mn. Evaluate sin(mx) cos(nx) dx. 1 A cos(m− n)x - cos(m+n)x] + C…

A: The objective is to find the correct option.

Q: 19. The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4…

A:

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: Find y dy ·S using the substitution u +5=√√y+2 y+2 © ²(√√y+2-5) (5√/y+2+y+24) + C…

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Q: Convert S.S. dzdydx 3-√√9-**-* Into an integral of spherical coordinates 319-x2

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Q: ·S- Find y dy Vy+2 using the substitutionu +5=√√y+2. A √y + 2 − 5 ) ( 5 √√y + 2 + y +24) + C (В…

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Q: Consider √(x-m. 3x5 -dx. Using the method of partial fractions, the given integral can be written as…

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Q: A -2 f Coxx dx x’sinx + 2x cosx – 2 dx + C

A: Using integration by parts,we got correct answer as option -(A)

Q: Question 18 Find the area bounded by the curve y 8 square units 4 square units 16 square units 10…

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Q: Consider ∫ x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?

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Q: The integral x dx x² + √x² can be transformed to which of the following using trigonometric…

A: ∫xx2+x2-1-1dx=∫secθ.secθtanθsec2θ+sec2-1-1dθ=∫sec2θtanθsec2θ-1+sec2-1dθ=∫sec2θtanθtan2θ+tanθdθ=∫sec2…

Q: What is the f(7) (-2) of f(x) = - +2x - 7x³ + ³² + 5x +1? 3x² 2

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Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

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: x² - 16 to fill in the table: - 4 5 4.5 4.1 4.01 Based on ONLY the table of values above, what…

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