Solve the integral: eln(2x²+3 +3x-4)³( (4x + 3)dx (2x²+3x+4)² + C A 4 (2x²+3x+4)*(4) 3 + C eIn(2x² + 3x-4) (4x+3) 3(2x²+3x-4) eln(2x²+3x-4)³ (2x²+3x-4) B с D + C + C

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: Find and sketch the domain of the function. f(x,y)=√y-x-8 Find the domain of the function. Express…

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Q: (3x + 5) dx 3 2 x³ -x²-x+1

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Q: To evaluate the integral sin³0cos ede by trigonometric transformation, we use the identity; 1-cos20…

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Q: Why does dA/dt = 0?

A: Since area is constant therefore dA/dt=0

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

A: We have to find volume

Q: Evaluate the double integral: (A) 40 B 30 C) 60 D) 80 ²(3x² +9y²) dxdy

A: The integration are.  .

Q: ,3 Which of the following can be determined given f(x) dx = 5, g(x) dx = 7, and ,3 [³h(x) d h(x) dx…

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Q: 7. f(x)= (4x²-3x5)7

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

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Q: -x/3 Jx/4 cscxcotxdx

A: topic- definite integral

Q: 10. Prove the identity: 2 + cot² (x) _ 1 = sin² x - csc² (x)

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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: Your cell phone plan charges a base charge each month plus a charge per daytime minute of usage. In…

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

A: Let's find volume of two curves rotating about x axis.

Q: Use V=SSSDdV and the substitutions u = x/a, v = y/b, w = z/c to show that the volume of the…

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

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Q: To evaluate the integral sin³0cos ede by trigonometric transformation, we use the identity; 1+ cos20…

A: topic- indefinite integral

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

A: A detailed solution is given below.

Q: 1 H 0 1 2 3 4 5 6 What are the domain and range of its inverse? O Domain: {y|1 ≤ y ≤5, ye R} and…

A: The domain of a function f(x) is the set of all possible values of x for which f is defined. The…

Q: Solve

A: We have to calculate the given indefinite integral

Q: 25 5+7x x dx

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Q: dy ssuming 5x³ +9y² − 4xy = 0 defines y as a differentiable function of x, use the theorem == dx Fy…

A: Given query is to find the derivative at indicated point.

Q: Find the slope of the line tangent to 2xy + π sin y = 2π through the point (1, π/2).

A: The slope of the line tangent to 2xy+πsin y=2π through the point 1,π2.

Q: If g(x) = -S^*[e²− ln(2t+1)]dt, find g''(x) . dx 2 (A (2x + 1)2 Be* -In(2x+1) 4 (C) Ce¹+ (2x + 1)² 4…

A: Here is the solution of the given problem.  By using derives under Integral.

Q: A population declines according to the model, 25,000(0,95) where A is the population t years after…

A: To solve the following problem

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: 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: Find the area enclosed by r = 2 sin 30.

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Q: 2x* dx

A: Here is the solution

Q: dx Transforming - using miscellaneous substitution will yield to secx + 1 A -dz 1+z² B 1² 2-2z² 1+z²…

A: Given problem:-

Q: 3. (D2 + 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

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Q: Transforming S Ⓒ / ² A 1-z² 1+z² ® / 12-2 B 1+z² © Ⓒ S ²¹²+² dz 1-z2 1+z² D S 1-z² dx secx + 1 -dz -…

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Q: (x-1)dx x(x²+1)(x² +2) S=

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Q: Why is it "h • db/t + b • dh/dt"  instead of   "h • dh/dt  + b • db/dt"?

A: Using Rule of differentiation.

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

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Q: (x²-3x+1) dx

A: Given that ∫23x2-3x+1dxSolution :∫23x2-3x+1dxx33-3x22+x23333-3322+3-233-3222+2

Q: alculate the amplitude and period of the function: f(x) = 3 sin(a) - 1 O Amplitude: 1, period: 2.…

A: Given query is to find the amplitude and the period of the function.

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

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Q: 10–f()=e" .sinh |2t. e-³¹ sin 2t -31 12- f(t) = t 14-f(t)=t² cos Zt. 16-f(t)=t² sin wt. = {0…

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Q: Q1/ From the following table of values, find the approximate value of f'(1.5) ? X 1.0 1.5 2.0 2.5…

A: Use the formula of derivatives and put all the values and calculate.

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: 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: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

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Q: I5 = 2 -3 x 0(x - 1)dx

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Q: Water stored in an inverted right circular cone leaks out at a constant rate of 2 ft3 per day. The…

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

A: Option (B) is the correct answer.

Q: tanx If f (x) = A B C D f √1+1² 0 1te¹ In (secx)√1+tan ²x 1+ e tanx 1+tan²x tanx 1+e sec 3x 1+ e…

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Q: C. Determine the Laplace transform of the following function f(x)=x² 1. 2. f(x) = ex, a ER

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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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