QUESTION 4 Evaluate › [ sin(lnx) dx' Integration by parts will be used repeatedly. What is the expression after the second integration by parts? 54 xsin (Inx) - xcos (Inx) - [sin (In x) dx + C O xsin (Inx) + xcos + xcos (Inx) - [sin (In x) dx + C O xsin (Inx) − xcos (Inx) + sin(In x) dx + C - O 2xsin (Inx) - sin (Inx) dx + C 4

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

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A: dsecθdθ= sec θ.tan θ

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

A: Please follow the next step.

Q: S = Consider O 14/3 O 17/6 O 5 0 6 3x5 3x4+6x³3x2 - 6x A B C • √(₁-1² + + + + ² S x-1 x+1 x+m d.…

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A: We have to find the limit

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A: As per our guidelines we are supposed to answer only one question i.e. question no (a). For the…

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

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A: We have to solve above integral

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A: To evaluate the integral

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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: What is the value of f(1) - 16B in ∫ x3 lnx dx = f(x) ( (1/4) lnx - B ) + C?

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Q: dx 3-2x-x2

A: Since, the student has posted multiple questions and mentioned to solve no. 5 but there is no no. 5…

Q: can be transformed to which of the following when trigonometric substitution is used? (x²+4)² sin ²0…

A: Please see the answer below.

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: 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: Evaluate tan" (x) sec¹x dx A B © D -tan (m+3)(x) + ¹ -tan (m+1)(x) + C m+3 m+1 −tan (m +1)(x) — —_¹…

A: This question can be solved using the concept of integration by substitution.

Q: QUESTION 8 Consider S S[x_m+ 17/6 5 6 14/3 3x5 -dx- Using the method of partial fractions, the given…

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

A: We have to solve above integral

Q: Evaluate (A) B ze Stan" (x) sec²x dx- D tan (+2)(x) +-tan" (x) + C tan (+3)(x) +tan (+1)(x) +C 1 1…

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Q: Exercises To Solve [No.5] OS s dx (x-1) √x²2x-3 3-2x-x²

A: Explained below

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A: Solution of the problem as follows

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Q: m-1 1 + m 1 m m+2 ¹tan (+2)(x) + —tan" (x) + C m-1 1 + m 1 m+3 Ɔ+ (*) (1 - 1)² + (x) (1 + m) U²1-…

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

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Q: Estimate the slope of the tangent line to the curve at the given point (-3.5,1.250) on the graph to…

A: In this question, we want to find the slope of the tangent line of the curve at point (-3.5, 1.250).

Q: QUESTION 16 The volume of the solid generated by revolving the region bounded by x²=4y and y2-4x…

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Q: Consider I x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? O 1/4…

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Q: Suppose m and n are constants and m #n. Evaluate A B C D [sin(mx) cos(nx) dx. [„ _m cos(m − n)x -…

A: Here's the solution, please have a look at it..

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A: We have to find out value

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

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A: Follow the procedure given below.

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: 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: 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

Q: Question 8 dx The integral s can be transformed to which of the following when trigonometric…

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Q: Let f(x)=2-3√. Then the expression can be written in the form where A, B, and C are constants.…

A: Solved below.

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

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