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

Q: Let T be the tetrahedron with vertices (4, 0, 0), (0, 5, 0), (0, 0, 5) and the origin. Write f(x, y,…

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Q: (B) 1 1 −tan (m+3)(x) + _—__——_—_tan (m + 1)(x) + C · m+3 m+1

A: Let us use trigonometric substitution. After solving we get correct answer is option-(B) as shown in…

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

A: Follow the procedure given below.

Q: Investigate the given function and graph it accurately. 1. y = x²-x+1 x-1 2. y = In - -1 x+5

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Q: Use Euler's method to solve the following ODES wwwwwwww dy dx = -2y + 4e¯*, with h = 0.18 from x = 0…

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

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Q: Suppose m and n are constants and m #n- Evaluate * sin(mx) cos(nx) dx cos(m+n)x] + C 1 −cos(m−n)x+·…

A: Indefinite Integration

Q: 2. A cheetah chase a deer which is 100 m ahead. The time in which the deer takes 10 leaps the…

A: We have to use simple logic to solve the problem

Q: Calculus Effect of Luxury Tax on Consumption Government economists of a developing country…

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

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Q: Question 1 What is the value of f(1) - 16B in fx³ Inx dx = f(x) ((1/4) Inx-B) + C? 12

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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)? (A) 3/8 B)…

A: We have to find out value

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

A: Integrating By Parts : ∫u.v dx =u∫v dx -∫dudx∫v dxdx

Q: Exercises To Solve [No.5] dx OS (x-1) √X²2X-3 dx 3-2x-x²

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Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Topic:- application of integration

Q: dx ·S can be transformed to which of the following when trigonometric substitution is used? (x²+4)²…

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

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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: Question 4 Evaluate sin (Inx) dx- Integration by parts will be used repeatedly. What is the…

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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- x² + sece tane de sece - 1 e integral sec²0 de 1+tan cose de 1-sin sine de S x dx can be…

A: We have to find the integral

Q: What is the value of f(1) - 168 in x3 Inx dx = f(x) ((1/4) Inx - B) + C? 02 8 8 0 3 1

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Q: Evaluate Stan" (x) sec¹x dx. 1 -tan (+2)(x) +-tan" (x) + C m+2 m 1 1 -tan (+1)(x) + -tan (™-1)(x) +…

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Q: Find the area bounded by the curve y = - -x³x²+3x and the line y=x. 16 4 (A) 10 square units B 8…

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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: (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: f(x) = x² + 5x - 1

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Q: Find the equation of the tangent line to the graph of the given function at the given value of x.…

A: Solved below.

Q: ·S- y dy Vy+2 using the substitution (√√y+2-5) (5√√y+2+y+21) +C 0²/(√y+2-5) (5√y+2+y+24) + C ○ ¾…

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Q: Consider the function f(x) shown in the graph below. (Note that you can click on the graph to get a…

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

A: topic - indefinite integral

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: Suppose m and n are constants and m #n. Evaluate I sin O 1 1 -cos(m-n)x- - cos(m+n)x+ C n-m m+n 1 1…

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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? O 0 01 2 со N 3 4

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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)? 3/8 1 1/2…

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Q: Question 2. Find the limit, if it exists, or show that the limit does not exist. (a) 4xy (2,3)—(0,0)…

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

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Q: Question Find the area of the region that is bounded above by the curve f(x) = (x + 8)2 and the line…

A: This question can be solved using the concepts of area bounded by curves.

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: Solution is here

Q: 19

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Q: Find the value of that will make the function ƒ(z) continuous everywhere. f(x) = 4z + k, -5 0 =…

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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: dx can be transformed to which of the following when trigonometric substitution is used? (x²+4)²…

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Q: 172. Evaluate the definite integral using the Fundamental Theorem of Calculus, Part 2. 3 La+…

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Q: Question 9 The integral S x dx x²+√√x²-1-1 A /co B / Ⓒece s cose de 1 - sine sec²0 de 1+ tane secᎾ…

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Q: Question 11 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

A: Explained below

Q: Evaluate Stan" (x) tan" (x) sec¹x dx

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Q: Find nd cos(z ² + y²)dA where D = {(x, y) | 16 ≤ x² + y² ≤ 81} D

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