x²+3x-7 X-2 +5x+31n|x-2|+C + +In|3x-6|+C 2 x²+5x+In/3x-6|+C x² + 5x + n/x-21 +C 2 3 In Evaluate the integral: Se x² A B D dx

Q: Evaluate the integral: Se3+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 - + C (3e)3 + cosh2x B…

A:

Q: Given the integral csc²u=cot²u+1 1+ cos2u 2 1-cos2u 2 sec²u=1+tan²u B cos²u=- sec (x-1) tan4…

A: According to our guidelines we can answer only one question or three subparts of a question. Other…

Q: 2x* dx

A: Here is the solution

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 +…

A:

Q: dx aluate: :S₁ (x+1) log(x+1) A In10 In[log(x+1)] + C 1 B -In[log(x+1)]+C In 10 O In 10 log² (x + 1)…

A: Topic:- application of integration

Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

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Q: If the Laplace transform of f(t) = e cos(et) + t sin(t) is determined the a. a shifting theorem can…

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Q: 2x ind the derivative of: 2e cos(8x). [Hint: use product rule and chain rule!] se e^x for e*. ow,…

A:

Q: To evaluate the integral [sin³0cos 60d0 by trigonometric transformation, we use the identity:…

A: ∫sin3θcos6θdθ

Q: X+2 Determine the case of the following proper rational function after simplification: (x²-4)(x³-8)…

A:

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

A:

Q: Question Find the volume of the solid whose base is a circle with radius 25 that has cross-sections…

A: Solution:

Q: Question 11 Let g be a differentiable function, and let the range of g be an interval 1. Suppose…

A: The integration are...

Q: Evaluate the improper integral 3 A 4 B O diverges N|9 름 12²233/30 dx

A:

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

A: The region bounded by the curves f(x)=ex, g(x)=e-x and x=3

Q: Evaluate the integral: A B C D H|m 1 6 1 |ო 3 √ sin S 1 6 sin(3x)cos(3x) dx

A:

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

A: Let's find useful formula for evaluation of integration.

Q: Question 5 The improper integral +∞0 5+0⁰ 0 ex dx is

A: We can solve this as follows:

Q: Evaluate: A B С) D (x+1) log(x+1) 1 -In[log(x+1)] + C In 10 1 -In 10 log² (x + 1) + C 2 In 10…

A: Given problem:-

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: Question 5 3 Evaluating √9-x² dx using trigonometric substitution will lead to: A 35*1/2 cos²0d0…

A:

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

A:

Q: Find the volume of solid generated by revolving the region bounded by f(x)=x²+1and g(x)=x²+2x+5about…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 1 x + × olve the integral: 5 ® shi+x+c A C 5 6 ® $h1+x+c B C © 6n|5+x²|+c C D Shi+x+c C dx

A:

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: To find the volume. Option B is correct.

Q: the integral: (u +3) du 1²5 -dx (3) √74³ cscxcotxdx

A: We have to find out integral

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: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: To evaluate the integral. Option A is correct.

Q: Fiind a33 of an arithmetic sequence if the common difference is -1 and a1=3

A:

Q: Using shell method, find the volume of R, when it is bounded by y = x³, x = 0, y = 8 about x- axis.

A: Shell method

Q: 4. f(x) √√3x52x + 7x² 18x-25 5. f(x) = (33x5-22)( 5x+13x4- 32x+51)

A:

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

A:

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

A: See the details solution in below

Q: +∞o fthe 0 The improper integral edx is

A:

Q: $²² Α) (1,∞0) B (-∞,1] (-∞0,00) Given D {0,1} dx, determine all value/values of P for which the…

A:

Q: Evaluate the double integral: A B NIG 5 3 m|p 99 In +10 2ydydx

A: To solve the following double integral

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3

A:

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

A:

Q: dx Evaluate: (x+1) log(x+1) 1 A In10 log² (x+1)+C 2 B -log² (x + 1) + C 2 In 10 In[log(x+1)] + C…

A: We have to integrate of given function

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

A: Now,The graph of the area bounded by f(x)=ex, g(x)=e-x and x=3 is shown below:

Q: integral sin ³0cos Odt sin20 2 sin²0 = 1 - cos²0 1+ cos20 cos²0= 2 1- cos20 (D) sin²0= 2 To evaluate…

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Q: Determine the area bounded by f(x)=x²-x and x-axis. 2 A unitz Ⓡunit² unit2 1 D 4 -unit²

A: We will integrate the f(x) between limits 0 to 1.

Q: Which of the following can be determined given f(x) dx = 5₁ x) dx = 5,₁ ₁ g(x)dx=7, and h(x) dx = -5

A:

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

A:

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: 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: 15+0. The improper integral e* dx is

A:

Q: Evaluate the improper integral (A) diverges B (Q) Na O ساح 3 1²23 -dx

A:

Q: Find the work done by the force field F(x, y) = x sin(y)i + yj on a particle that moves along the…

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Q: Question 32 Solve the integral: A) 3√√√x² +C (B) ex 3 2√x² +C с D 6√√x +C 3√x x² dx

A: