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

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

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Q: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

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Q: Solve sin² C cos²x = 1 on the interval 0 < x < 2T. -

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Q: 2x* dx

A: Here is the solution

Q: y = x Arccsc (+)

A: We have to to slove derivative

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

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Q: If g(x) = ªſ*'[e'− In(2t+1)]dt, find g ''(x) . - dx -2 4 A + (2x + 1)2 Be-In(2x+1) 2 C (2x + 1)² 4 D…

A: Given that,      gx=ddx∫-2xet-ln2t+1dt

Q: We can apply General Power Formula of Integration on which of the following integrals? I coshus / A…

A: In this question, we want to know that on which of the following integrals we can apply the general…

Q: dx (x+1) log(x+1) 1 -In[log(x+1)] + C In 10 -In 10 log2 (x+1)+C 2 In 10 In[log(x+1)] + C 1 Evaluate:…

A: To solve the following problem

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

A: To find the area bounded by curves

Q: Evaluate the triple integral: 3 2 1 S³ S² S²(x+y+z)dydxdz 0 A 12 B 18 C 6 D) 24

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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: Question 11 puas √1+1² Ffxx)=f -dt, then f'(x) equals 0 I+e' In(secx)√1+tan²x Itela tanx sec³x 1+ele…

A: Topic:- application of integration  Note :- as per our guideline if more than one question uploaded…

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

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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: Evaluate the double integral: S²² (3x² +9y²) dxdy 0

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Q: Question 3 In the indefinite Integral in(cosh. x +ex). sinh x +e* (A cosh x + ex sinh x + ex In(cosh…

A: The integration are

Q: Question 1 S A - -/-/- B If (0 dx (0+2)(x-1)² 12 93 -ja 12 3 - I 3 B -S[ = √( 14+2+ = -1 (1-12 4 +…

A: We can solve this as follows:

Q: 11 |_₁_f(x) dx = 0 and ² f(x)dx==1₁ 11 5 Given A Ⓡ 555 B 6 C D 킁킁 11 6 0 evaluate [²3f(x) dx -…

A: B option is correct.

Q: Question 4 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

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Q: Solve the integral: Seln(2x²+3x-4)²³ (4x + 3) dx (2x²+3x+4)4 (A) + C 4 B eln(2x²+3x-4)³ (4x+3)…

A: To solve the integral.

Q: Given √ 1 pdx.c A (-∞,1] B (1,00⁰) Ⓒ (-∞0,00) D (0,1) dx, determine all value/values of P for which…

A: This can be solved as follows:

Q: Given the integral sec (x - 1) tan4 (x-1)dx, which of the following equations will be useful for…

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

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Q: A lighthouse is on an island 400 meters off shore. The lighthouse beam makes a full turn every 15…

A: answer is in next step

Q: d [e'- In (21+1)]dt, find g(x) . dx -2 A ex-In(2x+1) 2 B ex_ (2x + 1)2 4 C (2x + 1)² 4 D (2x + 1)²…

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Q: |x-4|dx

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Q: 3 •√₁²³f(x)dx=5₁ ₁²9(x) g(x) dx = 7, and 1 3 h(x) dx = -5 Which of the following can be determined…

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Q: ff. W Ex] Let f(x) = 4x²+2x²+x+3 and :f(x), g(x) € 75[x] f(x). g(x). g(x) = 3x² + 3x²³² + 3x² + x…

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Q: tretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: To find the work done.

Q: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 1+ e'…

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Q: ₁₁³f(x)dx=5₁ g(x)dx=7, and 5, Which of the following can be determined given A [ (4f(x) + 9h(x) dx ®…

A: See the details solution in below

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

A: We need to choose correct option.

Q: Evaluate the double integral: A B D) 9|N 2 N|G m 100 3 8 •√x 1. √ √V 24 +10 2ydydx

A: Evaluating the double integral

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

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Q: Question 26 Determine the integral: x²cosxdx A x²sinx-2xcosx +2sinx + C B x²sinx + 2xcosx-2sinx + C…

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Q: Verify that * / II 21 ?х ду 224 ду ох - for f(x, y) = 4x4y3 - 6xy5.

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Q: Given B ₁ [_²_f(x) dx = 0 and [ f(x) dx = 11 2 55 6 D 0 11 11 = √²3f(x) dx - _2f(x) dx. evaluate

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Q: Evaluate the limit : lim √x+1-2 X-3 x²-9

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Q: A balloon is released fromthe ground 100 meters from an observer.The balloon rises directly upward…

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Q: Evaluate the definite integral by substitution: 21 1 dx 3/(1+3r)² (1) ² 3/1 + 13xdx 10 (3) [TV. (3)…

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Q: Consider the functions z = 6 ex In y, x= In (u cos v), and y = u sin v. əz əz (a) Express and du as…

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Q: Question 14 dx Transforming - using miscellaneous substitution will yield to secx + 1 1-z² A 1+z²…

A: Here we have to transform the given integral by using miscellaneous substitution.

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

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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: tanx f f(x) = = [tion. A B C √1+1² 1+e' In (secx)√1+tan²x tanx 1+e sec²x 1+ e tanx sec ³x tanx 1+e…

A: Integration

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

A: Here is the solution of the given problem. We solve this by using shell method

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

A: Given that                              I = ∫9x2+6x-7dx    we have to find correct choice for…

Q: Question 13 3 2 Evaluate the triple integral: f(x+y+z)dydxdz A) 24 B) 18 C) 6 D) 12

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