Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 1/4 3/8

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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Q: Find S- y dy Vy+2 using the substitution u +5=√√y+2.

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Q: ·S Evaluate 3x5 3x4+6x³-3x² - 6x -dx, using method of partial fractions.

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A: We know that integration of cosx is sinx +c. And integration of sinx is -cosx+c. Here i attached the…

Q: Suppose m and n are constants and m #n. Evaluate [sin (mx) cos (nx) dx.

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

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

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

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Q: Find S- y dy using the substitution u +5=√y+2. y+2 (A) (√3+2-5) (5√/F+2-1+24) +C 3 B…

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

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Q: What is the value of f(1)-168 in [x³ Inx dx = f(x) ((1/4) Inx-B) + C? A) 2 B) 1 (C) D) 3

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Q: The integral [₁ face 8 dx S can be transformed to which of the following when trigonometric…

A: We have to solve above integral

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Q: fe²x+lnx² sin x² dx = 25-410-312-2 2M 12 e2x cos x² dx

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

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Q: Evaluate tan" (x) secx dx. 1 A n(m + 1)(x). m+1 1 (В -tan (m + 2)(x) + m+2 1 -tan (m+1)(x). m+1 1…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)^2=2y, the…

A: Solution of the problem as follows

Q: pose m and n are const (-)+(+)x] + C m-n m+n [-cos(m-nx- -cos(m-n)x - cos(m + n)x] + C 1 m+n…

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Q: y dy √y+2 15. Find /y using the substitution u +5=√√y+2.

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

A: We have to find solutions

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 √ x³ Inx dx = f(x) ( (1/4) Inx - B) + C? О о O 3 02 01

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

A: Topic = Integration

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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: fx²cc use integration by parts. What is the expression after the second integration by parts? x2sinx…

A: Solved below.

Q: The integral I com S f se fse x dx x² + √√√x²-1. cose de 1-sin sinᎾ dᎾ 1+ cose sec²0 de 1+ tane sece…

A: Substitute x= secθ and solve . dsecθdθ = sec(θ) tan(θ).

Q: Question 21 y dy Find y+2 using the substitution +5= √y+2.

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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 Let…

Q: Question 3 Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is the…

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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 14 The integral x dx can be transformed to which of the following using trigonometric…

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Q: 3x5 ·S -dx- Using the method of partial fractions, the given integral can be written as 3x4+6x³3x² -…

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Q: Question 9 The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x…

A: Solution is here

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

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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: Find y dy S using the substitution u +5=√√y+2. √y+2 A (√9+2-5) (5√3+2-1+24) +0 B (√y+2-5)…

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

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

Q: QUESTION 7 Evaluate 3x5 3x4+6x³-3x² - 6x x²-2x-In O x²-4x 2 O x²-4x 2 O rẻ-2r 2 [(x-1) 1/6(x+2) 16/3…

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

A: Solution of the problem as follows

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Q: What is the derivative of the following? sin(t) d dt f 117 da cos(t) s(t) 4-sin² (t) 1 4 — sin² (t)…

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Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: To evaluate (A) (B resti x²cosx dx use integration by parts. What is the expression after the second…

A: In this question, we need to evaluate the given integral using integration by parts.

Q: Question 17 1/2 S. dx and using the substitution = x 1/2, the resulting integral takes the form:…

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Q: The integral O cose de 1-sine sec²0 de 1+ tan sece tane de sece - 1 S sine de 1+ cose x dx can be…

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