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 (x+1) 1/2 [(x-1) 1/6(x+2) 16/3- +In (x+1) 1/2 *(x-1) 1/6(x+2) 16/3 x+1 *(x− 1) 1/6(x+2) 16/3- -dx using method of partial fractions. ²]+C ¹¹²] + c -2) 16/3 J+C 29¹0¹²]+c +In - + mn[

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

A: Given

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

A:

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

A: We need to choose correct option.

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 only four integrals of the following integrals: 1/4 1 dx (i) dx (ii) J √1-9x² sin (3x) 0…

A:

Q: QUESTION 6 Suppose m and n are constants and m‡n. Evaluate 1 1 -sin(m-n)x+ -sin (n m-n m+n n+n)x] +…

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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: Exercises To Solve [N0.5] -2 05² = dx 2 x²+2x+5 5² 3dx 9x²-6x+5

A:

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: ³ SS ²0 Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), an

A:

Q: x ¹/2 dx and using the substitution y=x1/2, the resulting integral takes the form: x-x 4u -du…

A: We have given integral  I = ∫x12x-x3 dx u=x12 du=12x12-1 dx du=12x-12 dx du=12x12 dx 2du=dxx12…

Q: QUESTION 13 Find the area bounded by the trigonometric curves 3.667 square units 1.414 square units…

A:

Q: To evaluate x²cosx dx' x2sinx+2x cosx – 2 x2sinx+2x cosx – 2 x²sinx- – 2x cosx — 2 x2sinx – 2x…

A:

Q: 3x5 3x4+6x³-3x² - 6x B с -+ x-1 x+1 x+m S= Consider Sx-m+- A xm+-+- -dx. Using the method of partial…

A: Since the degree of the numerator is not less than degree of the denominator, perform polynomial…

Q: 3x5 3x4+6x3-3x2 - 6x uate -dx, using method of partial fractions. x²-2x O [ (x − 1) 1/6(x+2) 16/3 -…

A:

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: 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…

A:

Q: for the implicit equation zey +In(y) = x³-12? da dy 3x2 02-2 = xey + Y 3x² - ey dy da xey + What is…

A: Topic = Derivative

Q: When applying the u-substitution technique to this integral, we will need to exchange dx for du. 99…

A:

Q: Consider J x sinx cosx dx = f(x) sin2x-g(x) cos2x + C. What is the value of f(1) + g(1)? A) 1 B) 1/2…

A: We have to find the integral

Q: For the function y = (9x2 - 27)/x3 , determine the increasing and decreasing intervals, and identify…

A:

Q: dy 5.) dx -2x +y = ye +y = ye (ye*) ³ 1 е : ²³-7e²ce Ans: y³ 3X ce ³2

A:

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

A:

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

A:

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: 3x4+6x3-3x² - 6x + In 2-2x-In O x2−2x 2 -dx¹ (x-1) 1/6(x+2) 16/3 (x+1) 1/2 (x-1) 1/6(x+2) 16/3 (x+1)…

A:

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

A: Explained 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…

A:

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

A: Explained below

Q: ➡pose m and n are constants and m ‡n. Evaluate sin(mx) cos(nx) dx` 1 -cos(m-n)x- -cos(m+n)x] + C n-m…

A:

Q: waluate Stan" (x) sec¹x de m 1 m+3 −tan (m+3)(x) + 1 m+2 1 m+1 1 m+1 1 m+1 tan n (m+2)(x) + — tan”…

A: We will evaluate the given integral as shown below

Q: QUESTION 7 ·S sin²t sin²0 de csc³0 de sec ³0 de cos²0 de The integral dx (x²+4)² 01 Secto 0 + can be…

A:

Q: What value(s) of k in the equation y = ekx will satisfy the equation y + y' = y"?

A:

Q: ·S- sece tane de sece - 1 The integral S S x dx x²+√√√x²-1-1 sino de 1+ cos cose de 1-sino sec²0 de…

A: The objective is to find the correct option.

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

A:

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

A: Area bounded by the curve .

Q: Question 8 The integral - Ⓒ /se (B Sa / © S³ (D S x dx x² + √x² sece tane de sece - 1 cose de 1-sine…

A: We have to slove above integration

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

A:

Q: a) A vector equation of a line that goes through the points P(1, -3, 2) and Q(9, 2, 0)

A: topic- equation of line

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

A:

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

A:

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: What is the value of f(1) - 16B in | x³ Inx dx = f(x) ((1/4) Inx - B) + C? 00 O 3 0 2 01

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

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.…

A:

Q: To evaluate fx²cos x²cosx dx use integration by parts. What is the expression after the second…

A:

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…

A:

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…

A:

Q: Solve using Euler's Method dy dx sin(x+y) ex,y (0)-4, h-0.1 -

A:

Q: 3x5 Evaluate S 3x4+6x33x2 - 6x O x2−2x +In 2 x²-2x-In O x² - 4x 2 O x² - 4x 2 -dx, using method of…

A: Integration