Find the area bounded by the curve y=-x³ 1 - 16 A 8 square units B 16 square units 10 square units 4 square units 3 4 + 3x and the line y=x.

Q: Consider two athletes running at variable speeds v₁ (t) and v₂ (t). The runners start and finish a…

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Q: Evaluate 3 TIT 4xyzdxydydz O 15 O 15/2 10 о None of the choices

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Q: ve [No.5] -2 2 зах 9x²-6x+5

A: On solving this we will get

Q: To evaluate A B [x²cc x²cosx dx use integration by parts. What is the expression after the second…

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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)? 1/4 3/8…

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Q: Q4: Convert the following polar integral to Cartesian Integral in order (1) dx dy (2) dy dx T 6 csc0…

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Q: Consider x-m+ A 17/6 B 14/3 с 6 3x5 3x4+6x3 3x2 - 6x A B C + + x-1 x+1 x+m -dx. Using the method of…

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Q: y dy ³S- √y+2 3 3 0²/(√y+2-5)(-5√/y+2+y+21)+C © }(√y+2−5) (5√/y+2+y+21)+C (√y+2-5) (5√y+2-y+24)+C…

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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

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

A: Solution is here

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

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Q: For f x 1/2 dx and using the substitution=x1/2, the resulting integral takes the form: -du 411…

A: We know that integration of xn is nxn-1.   Here i attached the solution of this question.

Q: Find the area bounded by the trigonometric curves Ⓒ 3.450 square units O 2.828 square units O 1.414…

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Q: What is the value of f(1) - 16B in [x³ Inx dx = f(x) ((1/4) Inx - B) + C? (A) 1 B) 2 C) 0 D 3

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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: Evaluate Stan" (x) see³x dx

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Q: Evaluate sin (1 sin (Inx) dx Integration by parts will be used repeatedly. What is the expression…

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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: Evaluate tan tan" (x) sec¹x dx O 1 −tan (™+2)(x) + — tan” (x) + C m+2 m O 1 1 -tan (m + 1)(x) — — ¹…

A: To evaluate the integral

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: 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: 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

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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: 5. Evaluate the following triple integral. ſſſ (.x² + y² ) dx dy dz D D={(x,y):x² + y² ≤9.15:53)

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Q: S sec²0 do 1+tano seco tane de seco - 1 The integral O 1: S S x dx x²+√√√x²-1-1 coso do 1-sino sino…

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

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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? 01 3 00 02

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Q: For x 1/2 dx and using the substitution u=x1/2, the resulting integral takes the form: 4u -du 4-12…

A: We can solve the integral by using substitution .

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

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Q: A ²/ (√x+2-5) (5√y+2+y+21) + C 3

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

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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: 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: Estimate the slope of the tangent line to the curve at the given point (-0.5,4.998) on the graph to…

A: It is clearly seen in the figure that the tangent line is horizontal to the x axis at the point…

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)…

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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: Question 7 Consider S= Sx- x-m+ A) 5 3x5 3x4+6r³-3x²-6x A B C -+ -+- x-1 x+1 x+m 17/6 14/3 -dx.…

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

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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: 3x5 3x4+6x33x² - 6x Evaluate A B (C) (D) ·S= x²-2x-In x² - 4x 2 x² - 4x 2 x² - 2x 2 + In + In + In…

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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: 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 to…

A: Solution is here

Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: Suppose that Find f'(x). f'(x)= f(x+h)-f(x) = -5hx² +6hx + 2h²x + 3h² - 1h³.

A: We will solve the problem.

Q: Use the graph to find the following limits. a. lim f(x) b. lim f(x) x→1 x+3 a. Find lim f(x) or…

A: Here is the solution of the given problem. To, solve this problem we use the simple criteria of…