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

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

A: solution

Q: Question 13 Evaluate S A B 3x5 3x4+6x³ 3x² - 6x x² - 2x 2 - 4x 2 x² - 4x 2 -dx. using method of…

A: First of all note that:…

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 Let…

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

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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: or S- For x1/2 S- S- S- 411 dx and using the substitution -du -du -du 411 √4-(21²) 2 -du the…

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Q: ·S- y dy Find using the substitution u +5=√√y+2. √√y+2 ²² (√y+2-5) (5√/y+2+y+24) + C (√√y+2-5)…

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Q: Suppose m and n are constants and m‡n- Evaluate sin(mx) cos(nx) dx* 1 1 2n-m 1 -cos(m-n)x- +COS (m…

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Q: Exercises To Solve [No.5] 4 S (X-+1) √ X ²2X-3 3-2x-x²

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Q: 2 f sinx x2sinx + 2x cosx – 2 sinx dx + 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: For the function f(x) = x6 – 10x4 , find the points of inflection.

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Q: To evaluate x²cosx dx use integration by parts. What is the expression after the second integration…

A: We have to find the solutions

Q: Evaluate sin (Inx n(Inx) dx xsin (Inx) + xcos (Inx) - [sin (In x) dx+C _xsin (Inx) – xcos (lnx) –…

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Q: Question 4 What is the value of f(1) - 16B in J x³ Inx dx = f(x) ((1/4) Inx - B) + C? A) O B) 1 (C)…

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Q: Q4: Convert the following polar integral to Cartesian Integral in order (1) dx dy (2) dy dx T 6 csc0…

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Q: circular ring method. The formula for solving for the volume is given by V = - S" ₁ ( 1₂²-1²) · The…

A: Solution is here

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

A:

Q: Evaluate • O Stan" (x tan O m+1 1 m+3 1 m+2 m+1 "(x) sec¹x dx n (m + 1) (x) — __ ¹ (m+3)(x) + n (m +…

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Q: 1 3 Find the area bounded by the curve y== -x3. -x² + 3x and the line y=x. 16 10 square units 8…

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Q: consider ∫ xsinx cox dx= f(x) sin2x - g(x) cos2x + C. what is the value of f(1) + g(1)

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Q: QUESTION 4 To evaluate x²cosx dx' use integration by parts. What is the expression after the second…

A: The given integral is: I=∫x2cosxdx   Apply the integration by parts to solve the above integral.…

Q: Consider S √(x-m+ 14/3 B 5 Ⓒ17/6 D 6 3x5 3x4+6x³-3x² - 6x A B C + + x-1 x+1 x+m -dx. Using the…

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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…

A: Follow the procedure given below.

Q: Evaluate the integral ² ² sin² 20 r dr de where D = {(r, 0)| 0 ≤ 0 ≤ñ, 0≤ r ≤ 2√cos 20}. X

A: Solution: ∫∫Dr2sin2(2θ)rdrdθθ→0 to πr→0 to 2cos 2θ

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

A: using circular ring method evaluate the volume

Q: Suppose m and n are constants and 1 n-m 1 m-n m-n m‡n. 1 -cos(m− n)x- cos(m+n)x] + C m+n 1 -cos(m−…

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Q: ·S= Evaluate 3x5 3x4+6x³-3x² - 6x + In x² - 4x 2 x² - 4x 2 x²-2x-In x² - 2x 2 -dx using method of…

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Q: 3x5 dx Using the method of partial fractions, the given integral can be written as 3x² - 6x Consider…

A: To solve the following problem

Q: -S₁ Consider 08 14/3 O 17/8 05 3x5 3x4+6x³-3x²-6x •√(x-1 -dx- Using the method of partial fractions,…

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

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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: Washer Method

Q: x dx ·S- can be transformed to which of the following using trigonometric substitution? x²+√√x²-1-1…

A: Trigonometric substitution

Q: Evaluate A B Stan" (x) m+1 D "(x) sec4x dx. tan (+1)(x) +tan (-1)(x) + C m-1 tan (+1)(x)-tan (-1)(x)…

A: topic- indefinite integral

Q: The volume of the solid generated by revolving the region bounded by x squared equals 4 y and y…

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Q: dx The integral ·S= can be transformed to which of the following when trigonometric substitution is…

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Q: [ sin(mx) cos(nx) dx- D Suppose m and n are constants and m #n. Evaluate 1 1 A -cos(m-n)x- =…

A: This question can be solved using the concept of integration of trigonometric functions.

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

A: Here, the region is bounded by the curves x2=4y⇒x=4y & y2=4x which is rotated around y=4 axis…

Q: Given: 3z = xy_Find ƒ² + fy² +1 **+*+9 Option 1 Option 3 x²+y²+1 ²+²+3 9 Option 2 None of the…

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Q: -S- A Ⓡ / T B C S (D) S- For x1/2 dx and using the substitution u=x¹ x1/2, the resulting integral…

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Q: 3 Find the area bounded by the curve y= -x3x2+3x and the line y=x. 16 O 16 square units O 8 square…

A: Please follow the next step.

Q: he definition of the derivative, find f'(x). Then find f'(-3), f'(0), and f'(4) when the derivative…

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Q: = fx²coss x²cosx dx- use integration by parts. What is the expression after the second integration…

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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: Here is the solution of the given problem. We use here Washer Method

Q: Given the periodic function defined in one period by the function: (bt, f(t) = a, 0, 0 0. Provide…

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Q: y dy Find ·S= √y+2 0²/(√y+2-5)(-5√/y+2+y+21)+C 3 03 (√y+2-3) (5√/y+2+y+24) +C 3…

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Q: Find the area bounded by the curve y = 1x³ - 2x² + 3x and the line x3_ 16 16 square units 10 square…

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Q: Exercises To Solve [No.5] 3-2x-x²

A: Solved below.

Q: Question 18 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

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

Q: x1/2 ·S. dx and using the substitution = x1/2, the resulting integral takes the form: U (A) / -du…

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