van [ f(x)dx = 5, [_o(x)dx=7, and [_n(x) dx = - -5 Which of the following can be determined given A√xx)dx ® [²(4/(x) + 9h(x)) a © (f(x) - (x) dx Ⓒ [F(x) + g(x) + g(x) +h(x))ax

Q: X+2 Determine the case of the following proper rational function after simplification: (x² – 4)(x³ –…

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Q: Let f(x)=√3x-2 on the interval axis and find the volume of the resulting solid. 43л -unit 3 135 83…

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Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, th (A) 0 and…

A: Topic:- application of integration

Q: Determine the integral: x²cosxdx A x²sinx + 2xcosx-2sinx + C B x²sinx + 2xcosx + 2sinx + C…

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Q: Which integral below gives the volume of the solid of revolution obtained by rotating the bounded…

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Q: Find the area bounded by : f (x) =e*, g(x)=e¯* and x=3. A (e²-1)² e² sq. units (e³-1)² e3 sq. units…

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Q: - e*) sinh x + e* cosh x + ex In the indefinite Integral in(cosh x + ex). A In(cosh x + e*)- sinh x…

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Q: Solve the integral: A B C D 6√√x +C 3√x² + C 6 33³√/ x² +C √√√x 37 ကြ 3√x dx

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Q: The gradient at any point (x, y) of a curve is given by dy-3x² +ax-36 where a is a constant. The…

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Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

A: consider9x2+6x-7=9x2+6x+9-16=9(x+3)2-16 let u=x+3⇒du=dxThen9(x+3)2-16=9u2-16

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

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Q: 1 Solve the integral: J 3 x + x 5 6 x In|1+ A +C + C Shi+x+c 6 1+ C 5 1+x8 +c +C B C 516 In|1+ - dx

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Q: The improper integral ** ex dx is A Be (C) 1 D) 0 8

A: ∫0+∞e-x dx

Q: Evaluate the integral: Se³+ A B C 3+cosh2x33+cosh2x sinh2x dx (3e)3+cosh2x + C 2+2ln3 (3e)3+ sinh2x…

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Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: C option is false

Q: Find the volume of solid generated by revolving the region bounded by g(x)=x²+2x+ 5about the x-axis.…

A: Given:      fx=x2+1      gx=-x2+2x+5  Volume of solid revolving around the region is…

Q: (x+1)dx (x+2)(x-1)² 1 / S If B -√2-1 + + *(x-1)2 ]dx. +2 dx, the values of A & C respectively are:

A: We can solve this as follows:

Q: (x+1)dx (x+2)(x-1)² 2 . 93 15 S If (A (B) (c) D -- 9 9 9 2/3 W|N 3 A = -√ [14/2₂ B + x+2 x-1 +…

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Q: If (x+1) dx (x+2)(x-1)² S -=S= A B + x + 2 + x-1 C (x-1)2 dx, the values of A & C respectively are:

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0= A) infinitely many (B)…

A: We have to choose option find antiderivative

Q: 1 √√√√√x+x X Solve the integral: S- @ =√² m/1 + x ²³ / + c A C (1) 6in/5+ x ³²³| +C B © ²/³ m/1 + x…

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Q: We can apply General Power Formula of Integration on which of the following integrals? (A) Jeschuco…

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Q: 2 Let f(x)=√√3x-2 on the interval 1. Revolve the region between the curve, y=1 and y-axis about the…

A: To solve this problem we use cylindrical shell.. method.

Q: tanx If f (x) = A (В) (ⒸC) D - St 0 sec 3x 1+ e tanx In (secx) √ 1+tan ²x 1+ e tanx sec²x 1+elanx…

A: Finding the derivative of the integral

Q: Evaluating √√9-x² dx using trigonometric substitution will lead to: 57/2 A 18 "/2 cos²0d0 35*1/2 B…

A: ANS: B

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 C=/2 A 18 cos²0d0 (B) 1852/200…

A: See the details solution in below

Q: dx using miscellaneous substitution will yield to secx + 1 nsforming - S 1+2 / dz √²-22² dz 1+z²…

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Q: sinh x tex cosh x + ex In the indefinite Integral in(cosh x + ex)- sinh x tex (A) cosh x + ex B sinh…

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Q: In the indefinite Integral in(cosh x + e*). sinh x + ex cosh x + ex dx, what is the integrand?

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Q: Question 5 -S_(x + 1) dx A B (x + 2) (x - 1)² = √ [1+2+ = ²1+ x-1 If B -ia 9 9 W|N 1 9 3 1 9 3 دا |…

A: find out the value of A,B and C

Q: Given S dx, determine all value/values of for which the improper integral XP converges? (A) {0,1} B…

A: Please follow the next step.

Q: 9. For what value of k, k> 0, does (4kx-5k) dx = k² O 1 O 2 3 O 4

A: On solving this we will get

Q: + ∞o [** S The improper integral A B) 1 8 ex dx is

A: ∫0∞e-xdxSubstitute u=-x→dudx=-1→dx=-du=-∫euduWe know that ∫audu=auln(a)

Q: How many antiderivatives does a function of the form f(x) = x^ have when n0? (A) 1 B) none (C)…

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Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

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Q: sinh x + ex cosh x + ex In the indefinite Integral in(cosh x + ex)- dx, what is the integrand?

A: Intergrand

Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 1 A -unit² (B) unit² 1 H|m

A: Given that fx=x+13  and gx=x+1Solution :x+13=x+1x+13-x+1=0x+1x+12-1=0x+1=0 and x+12-1=0x=-1 and…

Q: The improper integral (A) e B) © ⒸO D 1 8 Stoe ex dx is

A: Given that,

Q: dx (x+1) log(x+ ) In[log(x+1)] + og² (x+1) + C

A: We have to choose the correct option from the given options

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: [/2cos²0do (A) 18 9[*/ cos²0d0 B…

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming S Ⓒ √ ²² +²2 dz (Α) -z²…

A: This question can be solved by substituting z=tanx2

Q: Question 27 Evaluate the double integral: (A) 80 B 30 с 40 D) 60 Question 28 Questions Filter (40) Y…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1

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Q: Which of the following can be determined given Ⓒx-d A (x) - )-g(x))dx (B S (4f(x) +9h(x))dx g(x)dx…

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Q: Question 2 Solve the integral: A √√x 3 B 33√/ x² +C 3√x² +C 6 6√√x +C D √√ 3√x dx

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Q: Evaluate the double integral: A 9 2 5 2 (В с D m|w 416 5² 5²² 2ydydx

A: A detailed solution is given below.

Q: sinh x tex + ex cosh x In the indefinite Integral in(cosh x + ex)- sinh x tex A In(cosh x + e*)-…

A: Answer: A

Q: Determine the area bounded by f(x) = x² − × a axis. A - unit² B unit² C unit² 2 -unit? +|5

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Q: 2+3x-7) X-2 dx Evaluate the integral: Se A²+ +In|3x-6|+C Ⓡ 1/²/₁ 2²+5x+! In/x-21 +C B 3 x²+5x+In…

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