π 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x = - to x = 4 4 (A) 1.414 square units B) 3.667 square units 2.828 square units D 3.459 square units

Q: Find the area bounded by the curve y=-x³ 1 - 16 A 8 square units B 16 square units 10 square units 4…

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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: S ' | Sc Sex²0 The integral dx (x²+4)² see c³0 de s²0 de csc ³0 de sin ²0 de can be transformed to…

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Q: (C) Find dx (i) y= for the following functions : 3x 2x-1 2x+1 (ii) y=sec(sec ¹5x)+e5lmx +4

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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

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A: We need to find rate of change of angle.

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

Q: S For x 1/2 x-x3 dx and using the substitutionu=x1/2

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Q: Use the quotient rule to find the derivative of the following. 2x-3 y= 7x+5

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Q: What is the approximate value of 24 that is found using the tangent line to at x = 16? Round to the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

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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: Solution is here

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

A: Volume of revolution

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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: The full solution of the question is given below:

Q: What is the value of f(1)- 168 in fx³ Inx dx = f(x) ((1/4) Inx-B) + C? A) 3 B 0 1 2

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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: ¡¡xaydx xexy dydx 10 Option 2 Option 1 e²+e=¹+3 e²+8²-3 e²-6-1-3 Option 3 None of the choices

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Q: Evaluate x2— 2x = In 4x–ܐ0x 3 5 3x4+ 63 - 3x2 -— 6x 2 O,2-4x 2 0 x²-2x 2 + ܀ -dx using method of…

A: Let's evaluate given integral.

Q: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Given problem:- Use double integral polar coordinates to find the area of the portion of the surface…

Q: -1/2 dx and using the substitution u=x1/2, the resulting integral takes the form: x-x -du -du S- @ /…

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Q: Sketch the curve of f(x), a function whose first derivative has the following properties. You must…

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

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Q: Evaluate the integral S√x Inx dx 3 2 4 -x² Inx+ x² + C 03x³nx-x²+c 4 2 -x² Inx+ 2 C 15 3 2 4 °²x²nx…

A: We have to solve above integral

Q: (5 Lim 9-5 dx S a -x²-8x-15

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Q: QUESTION 9 S x²-2x-In + In Evaluate 3x5 3x4+6x³-3x² - 6x O x2−2x 2 O x² - 4x O x² - 4x 2 て + In + In…

A: Solved below.

Q: Consider S x-m+ (A) 6 B) 5 3x5 3x4+6x³3x² - 6x A B C + + x-1 x+1 x+m 17/6 (D) 14/3 -dx. Using the…

A: Here is the solution of the given problem. Method of Partial Decomposition

Q: QUESTION 6 ·S. sece tane de sece - 1 The integral cose de 1-sine sec²0 de 1+tano sine de 1+ cose x…

A: Let's transform given integral.

Q: Find an equation of the line tangent to the graph of f(x) = (4x-7)(x+4) at (2,6). The equation of…

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Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

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

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

Q: QUESTION 5 Evaluate Sun"(x) seets de tan' ₁ (m + 2)(x) + tan m 1 -tan (m+3)(x) + · m+1 -tan…

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

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: S egral dx (x²+4)² can be transfa

A: Answer is option-(d).   Using basic equations of trigonometry and substitution we got the answer as…

Q: The height s (feet) of a ball hit into the air is given by s(t) = -16f² +50t + 5, where t is the…

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

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Q: In this problem, you are asked to carefully read Example 6.4.2 of APEX Calculus. 1 The given…

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Q: Suppose m and in are constants and m #n. Evaluate [sin(mx) cos(nx) dx Ⓒ![_!__cos (m-n)x+ ____cos(m +…

A: Here we have to find the integration of the given function.

Q: ·S= cost cose de . 1-sino sece tane de sec-1 The integral sine de 1+ cose sec²0 de 1+tano x dx can…

A: Let's transform integral by using trigonometric substitution.

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: QUESTION 19 A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are…

A: Solution of the problem as follows

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

A:

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

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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: 5ñ Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=to x== 4 (A) 3.667…

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Q: Question 12 What is the value of f(1) - 16B in [x³ Inx dx = f(x) ((1/4) Inx-B) + C? (A) 1 B) 3 2 D

A: Please see the below picture for detailed solution.

Q: What is the value of f(1) - 16B in ∫x^3 lnx dx= f(x) ( (1/4) lnx - B ) + C

A: To find out the required value.

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

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Q: QUESTION 8 The integral O S fec S S O O ·S- O x dx x²+√√√x²-1-1 sine de 1+ cose sec²0 de 1+tane cose…

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